diff --git a/docs/manual-checks.md b/docs/manual-checks.md
index 2c4467d..cc3a96a 100644
--- a/docs/manual-checks.md
+++ b/docs/manual-checks.md
@@ -269,33 +269,32 @@ single-process test can reach.
 
 Open the hosts screen without creating any group.
 
-**Pass:** the grid is the flat wrap of host cards it always was — no GROUPS section above it, no headings
-between the cards, no UNGROUPED, nothing saying the hosts are unfiled.
+**Pass:** the grid is the flat wrap of host cards it always was — no GROUPS section above it, no chip on any
+card, nothing saying the hosts are unfiled.
 
-**Failure means:** the "invisible until used" property is gone, and every existing user gets a heading they
-did not ask for. `RebuildSidebarRows` returns early when `Groups` is empty; that early return is the feature.
+**Failure means:** the "invisible until used" property is gone, and every existing user gets a section they
+did not ask for. `HasGroups` is what hides the row of group cards; `HostRowViewModel.HasGroup` hides the chip.
 
-### 3.2 Filing hosts, and folding a heading
+### 3.2 Filing hosts, and reading which group a card is in
 
-Make two groups, file some hosts into each through the host editor, then click a heading.
+Make two groups and file some hosts into each through the host editor.
 
-**Pass:** the heading's chevron flips and its hosts disappear; the count on the heading does not change,
-because it counts what is in the group rather than what is on screen. Clicking again brings them back.
-
-**Also check:** clicking a heading does not change which host is selected — the drawer stays open on the
-same machine and its EDIT and DELETE go on acting on it. This is asserted in a test, but the test drives the
-view model directly; what it cannot see is whether the `ListBox` writes something else back through the
-binding first.
+**Pass:** every filed card carries the group's name as an accent chip under its address; the cards stay one
+flat wrap, in one order, with nothing between them. **There is no heading and no fold on the desktop** — the
+headings, their chevrons and UNGROUPED are the phone's, whose list has no room for a row of group cards.
 
 **Then press a group card.** The grid narrows to that group's hosts, the card is marked as chosen, and
 SHOW ALL appears beside GROUPS. Pressing it brings the rest back and unmarks the card.
 
+**Failure means:** a full-width bar with a chevron between the cards is the old grouping coming back through
+`SidebarRows` — the desktop grid binds `VisibleHosts`. See `HostsScreen.axaml`.
+
 ### 3.3 Deleting a group with hosts in it
 
 Select a group with hosts and press DELETE.
 
 **Pass:** the question names how many hosts are filed under it and says they stay. Agreeing removes the
-group; the hosts reappear under UNGROUPED with everything else about them unchanged.
+group; the hosts lose their chip and are otherwise unchanged.
 
 **Failure means:** if the hosts vanish, the delete is rewriting host payloads, which it must not — see
 `HostGroupRepository`.
@@ -305,8 +304,8 @@ group; the hosts reappear under UNGROUPED with everything else about them unchan
 Make a group on machine A, file a host into it, sync. On machine B, sync, then delete the group and sync
 again. Back on A, sync.
 
-**Pass:** A shows the host under UNGROUPED. Open that host's editor: the group picker shows "(a group that is
-no longer here)" and *keeps it selected*. Change the port and save.
+**Pass:** A shows the host with no chip on its card, as though it were in no group. Open that host's editor:
+the group picker shows "(a group that is no longer here)" and *keeps it selected*. Change the port and save.
 
 **Failure means:** if the picker opened on "No group", saving has just unfiled the host — quietly, as a side
 effect of an unrelated edit. That is the case `BuildGroupChoices` adds the placeholder for.
@@ -642,33 +641,45 @@ Start 7.1's slow connection and press GIVE UP (or the tab's cross) while it is s
 opened — it is a real shell, and one running with nothing naming it would be worse than one that comes
 back.
 
-### 7.6 Dragging a host into a group · **least covered, like all drag and drop**
+### 7.6 Dragging a host onto a group card · **least covered, like all drag and drop**
 
-Make two groups and file a host into one. Drag a host card onto another group's heading; onto a host card
-inside another group; and onto UNGROUPED.
+Make two groups and file a host into one. Drag a host card up onto the other group's card.
 
-**Pass:** whatever is under the pointer washes accent while the pointer is over it, the cursor shows a move
-rather than a refusal, and the drop files the host — it moves under that heading and the counts on both
-headings change. Dropping onto its own group's heading is refused while still in the air.
+**Pass:** the group card under the pointer takes a two-pixel accent border while the pointer is over it, the
+cursor shows a move rather than a refusal, and the drop files the host — the chip on its card changes to the
+new group's name, the host counts under both group cards change, and the status line says where it went.
 
-**Failure means:** headless Avalonia cannot synthesise a platform drag, so nothing about this gesture is
-automated. The write it performs is: `MovingAHostToAGroup_FilesItAndLeavesItSelected`.
+**Also check three refusals**, each of which must show the "no" cursor and mark nothing: over the card of the
+group the host is *already* in; over another **host** card, which is deliberately not a target now that there
+are no headings to say which group it would mean; and over the empty space around the cards.
+
+**And getting a host back out** is the host's own editor — pick "No group" in its picker. There is no
+UNGROUPED target on the desktop any more, because there is no UNGROUPED heading for it to be.
+
+**And a drag held near the top or bottom edge of the grid scrolls it**, which is what makes this usable at
+all with forty machines: the group cards are the first thing in the scroller, and a drag cannot use the
+wheel. The pointer has to keep moving inside the band — a stationary pointer gets no drag events.
+
+**Failure means:** headless Avalonia cannot synthesise a platform drag, so the picking up, the cursor and
+the drop are covered by nothing. What *is* automated is the decision each drag event takes —
+`HostGridTests.TheGroupCardsAreWhatAcceptsADroppedHost` raises a real `DragOver` over both kinds of card —
+and the write at the end, `ShellFlowTests.MovingAHostToAGroup_FilesItAndLeavesItSelected`.
 
 ### 7.7 A click still selects, and a double click still connects
 
-Click host cards; drag one a few pixels without releasing; double-click one. Then double-click a group
-heading.
+Click host cards; drag one a few pixels without releasing; double-click one. Then double-click the space
+around the cards.
 
-**Pass:** a click selects, a small movement starts nothing, and a double click connects. Double-clicking a
-heading folds it and unfolds it again and connects to nothing.
+**Pass:** a click selects, a small movement starts nothing, and a double click connects. Double-clicking the
+space around the cards connects to nothing.
 
 **Failure means:** the 5-pixel threshold in `HostsScreen.axaml.cs` is not doing its job — the same failure
-as 2.16 on the other screen, and here it would make the grid unusable. A heading that connects means the
+as 2.16 on the other screen, and here it would make the grid unusable. Empty space that connects means the
 double-tap handler has lost its check that the pointer was over a card.
 
 ### 7.8 The highlight clears after a drag that goes nowhere
 
-Drag a host over a heading and release outside the grid, or press Escape mid-drag.
+Drag a host over a group card and release outside the grid, or press Escape mid-drag.
 
 **Pass:** the wash goes away.
 
@@ -676,7 +687,7 @@ Drag a host over a heading and release outside the grid, or press Escape mid-dra
 
 With host A selected, right-click host B and choose Delete.
 
-**Pass:** the question names **B**. Then right-click a group heading.
+**Pass:** the question names **B**. Then right-click the space around the cards.
 
 **Pass:** no menu opens at all, and the host selection has not moved.
 
diff --git a/src/DodoSSH.Client.App/App.axaml b/src/DodoSSH.Client.App/App.axaml
index 8ad5b88..80ad3eb 100644
--- a/src/DodoSSH.Client.App/App.axaml
+++ b/src/DodoSSH.Client.App/App.axaml
@@ -276,9 +276,12 @@
       <Setter Property="Background" Value="{StaticResource ChromeHover}" />
     </Style>
 
-    <Style Selector="Button.grouphead">
-      <Setter Property="Padding" Value="10,7,10,4" />
-    </Style>
+    <!--
+      Button.grouphead was here: the padding on the fold-away group heading that used to sit between the host
+      cards. The headings went when the grid became cards and the group cards above it became the thing that
+      names a group — see HostsScreen.axaml — and a style with nothing wearing it is a shape somebody will
+      later reintroduce by reaching for it.
+    -->
 
     <!-- A category in the vault's rail: the same accent strip a selected row carries, at full row height. -->
     <Style Selector="Button.cat">
@@ -661,19 +664,31 @@
     </Style>
 
     <!--
-      The row a host is about to be dropped on. A wash rather than the accent strip a selection carries,
-      because it is not a selection: it says "let go here", it lasts as long as the pointer is over the row,
-      and it has to be legible on top of whatever that row already looks like — including the selected row,
-      which is often the one being dragged onto.
+      The group card a host is about to be dropped on. A wash rather than the accent strip a selection
+      carries, because it is not a selection: it says "let go here", it lasts as long as the pointer is over
+      the card, and it has to be legible on top of whatever that card already looks like — including the
+      selected one, which is the group the grid is currently narrowed to and so often the one being dragged
+      onto.
+
+      Painted on the tile rather than on the item's own presenter, which is where this used to go when the
+      target was a full-width heading. A wash behind a 10-pixel-rounded tile is a square of colour with the
+      card floating on it — the same four grey corners the tiles list clears the theme's own hover and
+      selection brushes to avoid. Declared after that rule and after the selected-tile rule, because
+      Avalonia has no specificity and settles two matching rules by declaration order.
+
+      ◆ THE DOUBLED BORDER IS THE MARK, not the fill, and that is what the move to the tile forced. The fill
+      a selected tile already carries is the strongest one this palette has, so a target that only filled
+      would be invisible on the card the grid is narrowed to — which is the card a host most often has to be
+      dragged off, into another group. Two pixels of accent is legible on both.
 
       Set from the code-behind rather than by a binding, for the reason the whole gesture is code: the rows
       are rebuilt from scratch on every filter keystroke and every sync pass, so a flag on the view model
       would be state the list throws away halfway through the drag. See HostsScreen.axaml.cs.
     -->
-    <Style Selector="ListBoxItem.droptarget /template/ ContentPresenter#PART_ContentPresenter">
-      <Setter Property="Background" Value="{StaticResource AccentWash}" />
+    <Style Selector="ListBoxItem.droptarget Border.tile">
+      <Setter Property="Background" Value="{StaticResource Active}" />
       <Setter Property="BorderBrush" Value="{StaticResource Accent}" />
-      <Setter Property="BorderThickness" Value="0,0,0,2" />
+      <Setter Property="BorderThickness" Value="2" />
     </Style>
 
     <!--
diff --git a/src/DodoSSH.Client.App/Views/HostsScreen.axaml b/src/DodoSSH.Client.App/Views/HostsScreen.axaml
index 7cae392..2a589f7 100644
--- a/src/DodoSSH.Client.App/Views/HostsScreen.axaml
+++ b/src/DodoSSH.Client.App/Views/HostsScreen.axaml
@@ -151,8 +151,17 @@
 
       </StackPanel>
 
-      <!-- ============ THE GRID ============ -->
-      <ScrollViewer Grid.Row="3" HorizontalScrollBarVisibility="Disabled">
+      <!--
+        ============ THE GRID ============
+
+        A drop target that takes nothing itself. Everything the pointer can be over during a drag is inside
+        this control, and it has to accept one so that the group cards at the top of it stay reachable from
+        the bottom of a long grid: a host dragged off the fortieth card cannot be dropped on a group card
+        that has scrolled out of sight, so a drag held at either edge scrolls this while it is in flight.
+        See HostsScreen.axaml.cs.
+      -->
+      <ScrollViewer Grid.Row="3" x:Name="Scroll" HorizontalScrollBarVisibility="Disabled"
+                    DragDrop.AllowDrop="True">
         <StackPanel Margin="16,14" Spacing="16">
 
           <!-- ============ GROUPS ============ -->
@@ -198,10 +207,18 @@
               SelectedItem is GroupFilter and not SelectedGroup. The two are nearly the same thing here —
               GroupFilter assigns SelectedGroup — but only one of them may narrow the grid; see the property
               for why the phone's own use of SelectedGroup must not.
+
+              ◆ THESE CARDS ARE THE DROP TARGET. A host card dragged onto one is filed under that group, and
+              that is the whole of what a drag does on this screen. It used to be a heading inside the host
+              grid, and the headings are gone — see the note on the host grid below. A group is a thing that
+              is drawn once, at the top, where the eye already goes to narrow the grid; a target that is also
+              the label of what you are aiming at needs no explaining. See the code-behind for the gesture.
             -->
             <ListBox Classes="tiles" x:Name="GroupGrid"
+                     DragDrop.AllowDrop="True"
                      ItemsSource="{Binding Groups}"
-                     SelectedItem="{Binding GroupFilter}">
+                     SelectedItem="{Binding GroupFilter}"
+                     ToolTip.Tip="Press a group to show only its hosts. Drag a host card onto one to file it there.">
               <ListBox.ItemsPanel>
                 <ItemsPanelTemplate><WrapPanel /></ItemsPanelTemplate>
               </ListBox.ItemsPanel>
@@ -257,15 +274,31 @@
               focus off the terminal's child window and then calls Focus() on something that refuses it,
               leaving the window with nothing focused and the keystrokes going nowhere.
 
-              It binds SidebarRows rather than VisibleHosts, so the group headings are still in it. Two
-              reasons, and neither is decoration: a grid showing every group at once has to say which cards
-              belong to which, and a heading is the drop target that takes a host out of one group and into
-              another. See VaultViewModel.RebuildSidebarRows for why a heading is a row rather than a
-              container, and the code-behind for what a drag does with one.
+              ◆ CARDS ONLY, AND NO HEADINGS. It binds VisibleHosts rather than SidebarRows, which is the
+              collection with the group headings folded into it. Those headings were a full-width fold-away
+              bar between the cards — a chevron, a name and a count — and in a wrap of cards they read as a
+              collapsed dropdown that had somehow been dealt the hosts: the moment a first group existed the
+              grid stopped being a grid. Two controls saying "group" on one screen was one too many, and the
+              cards above are the better of the two. SidebarRows and the fold are still the phone's, whose
+              list has no room for a row of group cards; see Android's HostsScreen.
+
+              What a heading also was is the drop target, and that moved to the group cards rather than
+              going away with it — see the note on them above, and the code-behind for the gesture. A host is
+              taken back out of a group through its own editor, which is the one place "no group" can be said
+              plainly.
+
+              Which group a card is in is on the card, as a chip. That is what the heading above it used to
+              say, and one chip per card says it without an accordion.
+
+              SelectedItem is still SelectedSidebarRow and deliberately not SelectedHost, though every item
+              here is now a host. That property swallows the null the ListBox writes back whenever the
+              collection is rebuilt — which is every filter keystroke and every background sync — where
+              binding the host selection directly would let that null through, and a null host selection
+              closes the drawer and disarms a delete somebody is in the middle of confirming. See the
+              property, and RebuildVisibleHosts on where the real clearing is done.
             -->
             <ListBox Classes="tiles" x:Name="HostGrid" Focusable="True"
-                     DragDrop.AllowDrop="True"
-                     ItemsSource="{Binding SidebarRows}"
+                     ItemsSource="{Binding VisibleHosts}"
                      SelectedItem="{Binding SelectedSidebarRow}">
 
               <ListBox.ItemsPanel>
@@ -279,7 +312,8 @@
                 one per card: a ContextMenu inside a DataTemplate would have the row for its data context,
                 and the commands here are the vault's. The code-behind selects whatever was right-clicked
                 before the menu opens, so the selection-based commands act on the card under the pointer,
-                and cancels the menu outright over a group heading, which has no host to act on.
+                and cancels the menu outright over the space around the cards, where there is no host to act
+                on.
               -->
               <ListBox.ContextMenu>
                 <ContextMenu>
@@ -290,35 +324,9 @@
                 </ContextMenu>
               </ListBox.ContextMenu>
 
-              <ListBox.DataTemplates>
+              <ListBox.ItemTemplate>
 
-                <!--
-                  A heading, and it takes a whole row of the wrap rather than sitting in the flow as another
-                  card: it names the run of cards under it, and a heading the width of one card would read
-                  as the first of them. The stretch is what MinWidth buys — a WrapPanel gives a child the
-                  width it asks for and starts a new line when the line cannot hold it, so a child asking
-                  for more than one line holds is alone on its own.
-                -->
-                <DataTemplate DataType="vm:SidebarGroupHeader">
-                  <Button Classes="flat grouphead" MinWidth="640"
-                          Command="{Binding $parent[ListBox].((vm:VaultViewModel)DataContext).ToggleGroupCommand}"
-                          CommandParameter="{Binding}"
-                          HorizontalContentAlignment="Stretch">
-                    <Grid ColumnDefinitions="Auto,Auto,*">
-                      <TextBlock Grid.Column="0" Text="{Binding Chevron}"
-                                 Foreground="{StaticResource TextFaint}" FontSize="9"
-                                 VerticalAlignment="Center" Margin="0,0,6,0" />
-                      <TextBlock Grid.Column="1" Classes="label" Text="{Binding Label}"
-                                 Foreground="{StaticResource TextDim}" VerticalAlignment="Center"
-                                 TextTrimming="CharacterEllipsis" />
-                      <TextBlock Grid.Column="2" Classes="mono" Text="{Binding Count}" FontSize="11"
-                                 Foreground="{StaticResource TextFaint}" VerticalAlignment="Center"
-                                 Margin="8,0,0,0" HorizontalAlignment="Left" />
-                    </Grid>
-                  </Button>
-                </DataTemplate>
-
-                <DataTemplate DataType="vm:HostRowViewModel">
+                <DataTemplate x:DataType="vm:HostRowViewModel">
                   <Border Classes="tile">
                     <StackPanel Spacing="6">
                       <Grid ColumnDefinitions="Auto,*,Auto">
@@ -389,6 +397,26 @@
                                  VerticalAlignment="Top" Margin="6,3,0,0" />
                       </Grid>
 
+                      <!--
+                        The group this host is filed under, and only when it is filed under one — which is
+                        the same rule the group cards above follow, and the reason a keychain nobody has
+                        filed anything in looks exactly as it did before groups existed.
+
+                        This is what the fold-away heading over a run of cards used to say. A chip on the
+                        card says it per host instead, which is the shape the rest of this card already is
+                        and the shape a wrap of cards can carry: it survives the cards being reflowed, it
+                        needs no row of its own, and it is what changes when a card is dropped onto a group.
+
+                        Accent rather than plain, so the one chip that is a *place* is not read as another
+                        tag. A group whose name the vault cannot resolve leaves this empty rather than
+                        printing an id, for the reason a tag does. See HostRowViewModel.GroupLabel.
+                      -->
+                      <Border Classes="chip accent" Padding="5,0" HorizontalAlignment="Left"
+                              IsVisible="{Binding HasGroup}">
+                        <TextBlock Text="{Binding GroupLabel}" FontSize="9.5"
+                                   TextTrimming="CharacterEllipsis" />
+                      </Border>
+
                       <!--
                         The tags this host wears. Under the summary rather than beside it, because a host
                         can wear several and the line above is three fixed-width facts where these are not.
@@ -412,7 +440,7 @@
                   </Border>
                 </DataTemplate>
 
-              </ListBox.DataTemplates>
+              </ListBox.ItemTemplate>
             </ListBox>
 
             <!--
diff --git a/src/DodoSSH.Client.App/Views/HostsScreen.axaml.cs b/src/DodoSSH.Client.App/Views/HostsScreen.axaml.cs
index 82225b8..8c8734a 100644
--- a/src/DodoSSH.Client.App/Views/HostsScreen.axaml.cs
+++ b/src/DodoSSH.Client.App/Views/HostsScreen.axaml.cs
@@ -25,7 +25,7 @@ namespace DodoSSH.Client.App.Views;
 internal sealed partial class HostsScreen : UserControl
 {
     /// <summary>
-    /// How a host travels from the card it was picked up on to the heading it is dropped on.
+    /// How a host travels from the card it was picked up on to the group card it is dropped on.
     /// </summary>
     /// <remarks>
     /// An in-process format carrying the row itself, rather than text carrying an id. The drag never leaves
@@ -43,6 +43,21 @@ internal sealed partial class HostsScreen : UserControl
     /// </remarks>
     private const double DragThreshold = 5;
 
+    /// <summary>How close to the top or bottom of the grid a drag has to be held to scroll it.</summary>
+    /// <remarks>
+    /// Deeper than a card's own margin, because the band has to be reachable while the pointer is still
+    /// carrying something the user is looking at — a band the width of a hairline would only be found by
+    /// accident, and only by somebody who did not need it.
+    /// </remarks>
+    private const double EdgeBand = 48;
+
+    /// <summary>How far one drag event inside that band moves the grid.</summary>
+    /// <remarks>
+    /// Roughly a third of a card, so a pointer moving inside the band travels the grid at about the speed it
+    /// is moving. A step of a whole card would jump the target out from under the pointer between two events.
+    /// </remarks>
+    private const double EdgeStep = 24;
+
     /// <summary>The press a drag would start from, or null once it has become one or been let go of.</summary>
     /// <remarks>
     /// Held because <see cref="DragDrop.DoDragDropAsync"/> takes the press rather than the movement: the
@@ -55,7 +70,7 @@ internal sealed partial class HostsScreen : UserControl
 
     private Point origin;
 
-    /// <summary>The card or heading the pointer is currently over, while a drag is in flight.</summary>
+    /// <summary>The group card the pointer is currently over, while a drag is in flight.</summary>
     private ListBoxItem? marked;
 
     public HostsScreen()
@@ -78,9 +93,22 @@ internal sealed partial class HostsScreen : UserControl
         HostGrid.PointerReleased += OnPointerReleased;
         HostGrid.PointerCaptureLost += OnPointerCaptureLost;
 
-        DragDrop.AddDragOverHandler(HostGrid, OnDragOver);
-        DragDrop.AddDragLeaveHandler(HostGrid, OnDragLeave);
-        DragDrop.AddDropHandler(HostGrid, OnDrop);
+        // The host grid is where a drag starts and the group cards are where it lands. They used to be the
+        // same control: the target was a heading among the cards, and with the headings gone the group cards
+        // are the only thing on this screen that names a group. A card dropped onto another card is refused
+        // rather than filed beside it — in a grid with no headings there is nothing to say which group that
+        // would be, and a gesture whose result you cannot see before you let go is one that files machines
+        // somewhere the user did not intend.
+        DragDrop.AddDragOverHandler(GroupGrid, OnDragOver);
+        DragDrop.AddDragLeaveHandler(GroupGrid, OnDragLeave);
+        DragDrop.AddDropHandler(GroupGrid, OnDrop);
+
+        // Everywhere else the pointer can be during a drag, and it is a handler rather than the absence of
+        // one because AllowDrop is an inherited property: it is set on the scroller so that a drag anywhere
+        // over the grid is reported at all, and that makes every card inside it a drop target as far as the
+        // platform is concerned. This is where all of them but a group card are turned down — and where a
+        // drag held at the top or bottom edge pulls the grid towards the target.
+        DragDrop.AddDragOverHandler(Scroll, OnDragOverScroll);
     }
 
     /// <remarks>
@@ -117,9 +145,9 @@ internal sealed partial class HostsScreen : UserControl
     /// </remarks>
     private void OnHostActivated(object? sender, TappedEventArgs e)
     {
-        // Only over a card. A double-tap on a group heading folds it and unfolds it again, and must not also
-        // connect to whichever host was selected before — which is what an unguarded handler would do, on a
-        // machine the user is not even pointing at.
+        // Only over a card. A double-tap on the space around them must not connect to whichever host was
+        // selected before — which is what an unguarded handler would do, on a machine the user is not even
+        // pointing at.
         if (Vault is { } vault && RowUnder(e.Source) is HostRowViewModel)
         {
             _ = vault.ConnectCommand.ExecuteAsync(null);
@@ -137,9 +165,9 @@ internal sealed partial class HostsScreen : UserControl
     /// against.
     /// </para>
     /// <para>
-    /// Cancelled outright over a group heading and over the space around the cards. Neither is a host, and a
-    /// menu offering Connect, Edit and Delete over one would be three buttons that either do nothing or act
-    /// on something else entirely.
+    /// Cancelled outright over the space around the cards. That is not a host, and a menu offering Connect,
+    /// Edit and Delete over it would be three buttons that either do nothing or act on something else
+    /// entirely.
     /// </para>
     /// </remarks>
     private void OnContextRequested(object? sender, ContextRequestedEventArgs e)
@@ -233,9 +261,9 @@ internal sealed partial class HostsScreen : UserControl
     /// Says whether what is under the pointer would take this host, and marks it if it would.
     /// </summary>
     /// <remarks>
-    /// A host over its own group's heading is refused, which is not pedantry: <c>DragDropEffects.None</c> is
-    /// what turns the cursor into the "no" one, and a drag that looks like it would do something and then
-    /// does nothing is worse than one that says so while it is still in the air.
+    /// A host over the card of the group it is already in is refused, which is not pedantry:
+    /// <c>DragDropEffects.None</c> is what turns the cursor into the "no" one, and a drag that looks like it
+    /// would do something and then does nothing is worse than one that says so while it is still in the air.
     /// </remarks>
     private void OnDragOver(object? sender, DragEventArgs e)
     {
@@ -254,6 +282,60 @@ internal sealed partial class HostsScreen : UserControl
 
     private void OnDragLeave(object? sender, DragEventArgs e) => Unmark();
 
+    /// <summary>
+    /// Carries the grid under a drag that is over the cards rather than over a group.
+    /// </summary>
+    /// <remarks>
+    /// <para>
+    /// <b>Without this the gesture is only available to whoever can see both ends of it.</b> The group cards
+    /// are the first thing in the scrolling stack and the host being filed may be the fortieth card down, and
+    /// a drag cannot use the wheel — the pointer button is held. So a drag held near the top edge pulls the
+    /// grid down towards the target, which is what every file manager does with a drag near the edge of a
+    /// list.
+    /// </para>
+    /// <para>
+    /// A step per event rather than a timer, and that is a real limit rather than a simplification: a
+    /// stationary pointer receives no drag events on any platform this runs on, so the scroll follows the
+    /// pointer moving inside the band and stops when it stops. A timer would scroll on its own and would then
+    /// need cancelling on the drop, on the leave, and on the drag that ends outside the window entirely.
+    /// </para>
+    /// <para>
+    /// Reached only when the group cards did not handle the event first, which is what makes refusing the
+    /// drop here correct: the space around the cards is not a target, and saying so keeps the "no" cursor on
+    /// everything that is not a group.
+    /// </para>
+    /// </remarks>
+    private void OnDragOverScroll(object? sender, DragEventArgs e)
+    {
+        if (e.DataTransfer.TryGetValue(HostFormat) is null)
+        {
+            return;
+        }
+
+        e.Handled = true;
+        e.DragEffects = DragDropEffects.None;
+        Unmark();
+
+        var at = e.GetPosition(Scroll).Y;
+        var height = Scroll.Bounds.Height;
+
+        var step = at switch
+        {
+            _ when at < EdgeBand => -EdgeStep,
+            _ when at > height - EdgeBand => EdgeStep,
+            _ => 0,
+        };
+
+        if (step == 0)
+        {
+            return;
+        }
+
+        var furthest = Math.Max(0, Scroll.Extent.Height - Scroll.Viewport.Height);
+
+        Scroll.Offset = Scroll.Offset.WithY(Math.Clamp(Scroll.Offset.Y + step, 0, furthest));
+    }
+
     /// <remarks>
     /// Fire-and-forget, like every other command this control runs: the move writes to the vault and reports
     /// itself onto the status line, and a drop handler that awaited it would be an event handler returning a
@@ -279,13 +361,12 @@ internal sealed partial class HostsScreen : UserControl
     /// </summary>
     /// <remarks>
     /// <para>
-    /// A heading is the obvious target and a card is the useful one: dropping onto a machine files the
-    /// dragged host beside it, which means the whole band of cards under a heading is a target rather than
-    /// one line of text. The ungrouped heading is a target like any other, and it is how a host is taken out
-    /// of a group without opening the editor.
+    /// One kind of target: a group card. It is the control that already answers "which group", it is drawn
+    /// at the top of the screen where a drag can reach it from anywhere in the grid, and what it does when
+    /// dropped on is what it says on it. The space around the cards takes nothing.
     /// </para>
     /// <para>
-    /// A group the vault no longer has is read as no group at all, which is what the grid already does with
+    /// A group the vault no longer has is read as no group at all, which is what the list already does with
     /// a dangling reference — see <c>VaultViewModel.RebuildSidebarRows</c>. That is decided in the command
     /// rather than here, so the rule has one home.
     /// </para>
@@ -293,25 +374,13 @@ internal sealed partial class HostsScreen : UserControl
     private static DropTarget? Target(DragEventArgs e)
     {
         if (e.DataTransfer.TryGetValue(HostFormat) is not { } dragged
-            || Container(e.Source) is not { } container)
+            || Container(e.Source) is not { DataContext: HostGroupRowViewModel group } container
+            || dragged.Host.GroupId == group.EntityId)
         {
             return null;
         }
 
-        Guid? group = container.DataContext switch
-        {
-            SidebarGroupHeader header => header.GroupId,
-            HostRowViewModel row => row.Host.GroupId,
-            _ => null,
-        };
-
-        if (container.DataContext is not (SidebarGroupHeader or HostRowViewModel)
-            || dragged.Host.GroupId == group)
-        {
-            return null;
-        }
-
-        return new DropTarget(dragged, group, container);
+        return new DropTarget(dragged, group.EntityId, container);
     }
 
     private void Mark(ListBoxItem container)
@@ -353,5 +422,10 @@ internal sealed partial class HostsScreen : UserControl
         : null;
 
     /// <summary>A drag in flight, and where it would land.</summary>
-    private sealed record DropTarget(HostRowViewModel Host, Guid? GroupId, ListBoxItem Container);
+    /// <remarks>
+    /// The group is a <see cref="Guid"/> rather than a nullable one, which it was while the ungrouped
+    /// heading was also a target. Every target is now a group card and every group card has an id; the way
+    /// out of a group is the host's own editor, which is the one place "no group" can be said in words.
+    /// </remarks>
+    private sealed record DropTarget(HostRowViewModel Host, Guid GroupId, ListBoxItem Container);
 }
diff --git a/src/DodoSSH.Client.Shell/ViewModels/VaultViewModel.cs b/src/DodoSSH.Client.Shell/ViewModels/VaultViewModel.cs
index de12ffd..3849b4e 100644
--- a/src/DodoSSH.Client.Shell/ViewModels/VaultViewModel.cs
+++ b/src/DodoSSH.Client.Shell/ViewModels/VaultViewModel.cs
@@ -222,6 +222,31 @@ internal sealed partial class HostRowViewModel(
     /// <summary>Whether this row has a vault to name.</summary>
     internal bool HasVaultBadge => VaultBadge.Length > 0;
 
+    /// <summary>
+    /// The name of the group this host is filed under, or empty for a host that is in none.
+    /// </summary>
+    /// <remarks>
+    /// <para>
+    /// What the desktop's grid draws as a chip on the card. It is the one thing the fold-away group headings
+    /// between the cards used to say, and the reason removing them cost nothing: a card that names its own
+    /// group answers the question per host, where a heading answered it per run of cards and needed the grid
+    /// to be sorted into runs to do it. The phone still draws headings — its list has no room for the row of
+    /// group cards the desktop puts above the grid — so <see cref="SidebarGroupHeader"/> stays.
+    /// </para>
+    /// <para>
+    /// Resolved once when the list is built, like <see cref="TagLabels"/> and for the same two reasons: the
+    /// row stores an id and a chip shows a name, and the answer cannot change without the list being rebuilt.
+    /// <b>A group id that does not resolve leaves this empty</b> rather than printing the id — the reference
+    /// is allowed to dangle, deleting a group deliberately does not rewrite the hosts in it, and "the group
+    /// this names is not here" and "this names no group" are the same thing to look at. See
+    /// <see cref="HostSecret.GroupId"/>.
+    /// </para>
+    /// </remarks>
+    internal string GroupLabel { get; init; } = string.Empty;
+
+    /// <summary>Whether this host is filed under a group the vault can name.</summary>
+    internal bool HasGroup => GroupLabel.Length > 0;
+
     internal HostSecret Host => host.Secret;
 
     /// <summary>
@@ -1051,8 +1076,8 @@ internal sealed partial class VaultViewModel(
             "No hosts yet. Press + NEW HOST to add one, or import the machines already in this computer's "
             + "~/.ssh/config from Preferences.",
         (_, not null, 0) =>
-            "Nothing is filed under this group yet. Drag a host onto its heading in the grid, or choose the "
-            + "group in a host's own editor.",
+            "Nothing is filed under this group yet. Press SHOW ALL, then drag a host card onto this group's "
+            + "card — or choose the group in a host's own editor.",
         _ => "No host matches that. The name, the address and the notes are all searched.",
     };
 
@@ -2358,6 +2383,12 @@ internal sealed partial class VaultViewModel(
                     // Only when there is something to tell apart. A badge on every row of a
                     // single-vault list is noise that says the same thing on all of them.
                     VaultBadge = several ? vault.Name.ToUpperInvariant() : string.Empty,
+
+                    // Every readable vault's groups, not the active one's, because a host in a team's
+                    // vault is filed under that team's group — and looked up here rather than on the row
+                    // for the reason the tag names are: the map is the list's, and a row that reached for
+                    // it would be a lookup per chip per redraw.
+                    GroupLabel = GroupLabelFor(item.Secret.GroupId),
                 }));
         }
 
@@ -2674,6 +2705,17 @@ internal sealed partial class VaultViewModel(
             .OrderBy(label => label, StringComparer.CurrentCulture),
     ];
 
+    /// <summary>
+    /// The name behind a host's group id, or empty where there is none to show.
+    /// </summary>
+    /// <remarks>
+    /// Empty covers both "this host is in no group" and "the group it names is not in this vault any more",
+    /// which is the same answer the list gives a dangling reference everywhere else. See
+    /// <see cref="HostRowViewModel.GroupLabel"/>.
+    /// </remarks>
+    private string GroupLabelFor(Guid? groupId) =>
+        groupId is { } id && groupsById.TryGetValue(id, out var group) ? group.Label : string.Empty;
+
     /// <summary>Refills <see cref="Groups"/>, counting the hosts filed under each.</summary>
     private void RebuildGroups()
     {
@@ -2857,10 +2899,10 @@ internal sealed partial class VaultViewModel(
     /// </summary>
     /// <remarks>
     /// <para>
-    /// What dragging a row onto a heading does, and the only thing in this application that changes a host
-    /// without opening the editor. That is the justification for it existing at all: filing thirty imported
-    /// machines meant thirty rounds of open, pick, save, and the field being changed is the one field of a
-    /// host that is about arrangement rather than about the machine.
+    /// What dragging a host card onto a group card does, and the only thing in this application that changes
+    /// a host without opening the editor. That is the justification for it existing at all: filing thirty
+    /// imported machines meant thirty rounds of open, pick, save, and the field being changed is the one
+    /// field of a host that is about arrangement rather than about the machine.
     /// </para>
     /// <para>
     /// It writes the saved host rather than the editor's contents, and refuses while the editor is open. A
diff --git a/tests/DodoSSH.Client.App.Layout.Tests/HostGridTests.cs b/tests/DodoSSH.Client.App.Layout.Tests/HostGridTests.cs
index 28a02e9..f34a3cc 100644
--- a/tests/DodoSSH.Client.App.Layout.Tests/HostGridTests.cs
+++ b/tests/DodoSSH.Client.App.Layout.Tests/HostGridTests.cs
@@ -2,6 +2,7 @@ using Avalonia;
 using Avalonia.Controls;
 using Avalonia.Headless;
 using Avalonia.Input;
+using Avalonia.Interactivity;
 using Avalonia.VisualTree;
 using DodoSSH.Client.App.Views;
 using DodoSSH.Client.Session;
@@ -127,30 +128,85 @@ public sealed class HostGridTests : IAsyncLifetime
     }
 
     /// <remarks>
-    /// A heading is an item in the same list and the control will happily select it, but it is not a host —
-    /// and a menu offering Connect, Edit and Delete over one would be three entries that either do nothing
-    /// or act on a machine somewhere else in the grid.
+    /// <para>
+    /// The space around the cards is part of the same <c>ListBox</c>, and a menu offering Connect, Edit and
+    /// Delete over it would be three entries acting on whichever machine happened to be selected — which is
+    /// the whole mistake this handler exists to prevent, reached by clicking nothing at all.
+    /// </para>
+    /// <para>
+    /// Raised on the list itself rather than clicked at a point known to be empty. What the handler reads is
+    /// the event's source, and a source that is the list rather than an item is exactly what the empty space
+    /// produces; a coordinate would additionally be asserting where the wrap put the cards.
+    /// </para>
     /// </remarks>
     [Fact]
-    public async Task ARightClickOnAGroupHeadingOpensNothingAndMovesNothing()
+    public async Task ARightClickOffAnyCardOpensNothingAndMovesNothing()
     {
-        await OnTheGridAsync((screen, window) =>
+        await OnTheGridAsync((screen, _) =>
         {
             var selected = Row(vault, "prod-db");
             vault.SelectedHost = selected;
 
-            var heading = screen.HostGrid
-                .GetVisualDescendants()
-                .OfType<ListBoxItem>()
-                .First(item => item.DataContext is SidebarGroupHeader);
-
-            RightClick(heading, window);
+            screen.HostGrid.RaiseEvent(new ContextRequestedEventArgs
+            {
+                RoutedEvent = Control.ContextRequestedEvent,
+                Source = screen.HostGrid,
+            });
 
             vault.SelectedHost.ShouldBeSameAs(selected, "the selection the menu would have acted on");
             screen.HostGrid.ContextMenu.ShouldNotBeNull().IsOpen.ShouldBeFalse();
         });
     }
 
+    /// <summary>
+    /// A host held over a group card would be filed there, and one held over another host card would not.
+    /// </summary>
+    /// <remarks>
+    /// <para>
+    /// The group headings that used to sit between the cards are gone — see
+    /// <c>ScreenLayoutTests.TheHostsGridHoldsCardsAndNoGroupHeadings</c> — and with them went the thing a
+    /// dragged host was dropped onto. This holds the replacement in place, and the refusal with it: a card
+    /// dropped onto another card used to file it beside that one, which was legible while a heading said
+    /// which group the band of cards belonged to and is guesswork now that none does.
+    /// </para>
+    /// <para>
+    /// What is <em>not</em> here is the platform's half — picking the card up, the cursor, the drop itself.
+    /// Headless Avalonia has no native window and can synthesise none of it. The write at the end of the
+    /// gesture is <c>ShellFlowTests.MovingAHostToAGroup_FilesItAndLeavesItSelected</c>, and what neither
+    /// covers is in docs/manual-checks.md 7.6.
+    /// </para>
+    /// </remarks>
+    [Fact]
+    public async Task TheGroupCardsAreWhatAcceptsADroppedHost()
+    {
+        await OnTheGridAsync((screen, _) =>
+        {
+            var carried = new DataTransfer();
+            carried.Add(DataTransferItem.Create(HostFormat, Row(vault, "prod-db")));
+
+            var onto = screen.GroupGrid
+                .GetVisualDescendants()
+                .OfType<ListBoxItem>()
+                .Single(item => item.DataContext is HostGroupRowViewModel);
+
+            var over = Over(onto, carried);
+
+            onto.Classes.ShouldContain("droptarget", "the card says it would take the host");
+            over.DragEffects.ShouldBe(DragDropEffects.Move);
+
+            var refused = Over(CardFor(screen, Row(vault, "stage-web")), carried);
+
+            refused.Handled.ShouldBeTrue("the screen answered rather than leaving it to the platform");
+            refused.DragEffects.ShouldBe(
+                DragDropEffects.None,
+                "a card dropped onto another card would be filed somewhere nothing on screen names");
+
+            // And the group card it was over a moment ago stops offering to take it, which is the half of
+            // this that is wrong far more often than the mark appearing at all.
+            onto.Classes.ShouldNotContain("droptarget");
+        });
+    }
+
     /// <remarks>
     /// Pressing a group card narrows the grid to that group, and pressing SHOW ALL brings the rest back.
     /// Driven through the property the card's <c>ListBox</c> binds rather than through a click, because
@@ -182,6 +238,32 @@ public sealed class HostGridTests : IAsyncLifetime
 
     // ---- Helpers ----
 
+    /// <summary>The same in-process format the screen's own drag carries.</summary>
+    /// <remarks>
+    /// Declared again here rather than made visible, because what the two have in common is the contract —
+    /// the name and the type — and a test holding the screen's own field would go on passing if the screen
+    /// started carrying something else under it.
+    /// </remarks>
+    private static readonly DataFormat<HostRowViewModel> HostFormat =
+        DataFormat.CreateInProcessFormat<HostRowViewModel>("dodossh-host-row");
+
+    /// <summary>Holds a dragged host over one control and returns what the screen said about it.</summary>
+    /// <remarks>
+    /// The nearest a headless test gets to the gesture. No platform drag can be synthesised — there is no
+    /// native window to start one — but <c>DragOver</c> is an ordinary routed event, and it is where every
+    /// decision this screen makes about a drop is taken: whether the thing under the pointer would accept
+    /// the host, and whether it is marked while it is being held there. The drop itself only repeats that
+    /// question and runs the command. See docs/manual-checks.md 7.6 for what is left over.
+    /// </remarks>
+    private static DragEventArgs Over(Interactive target, DataTransfer carried)
+    {
+        var over = new DragEventArgs(DragDrop.DragOverEvent, carried, target, default, KeyModifiers.None);
+
+        target.RaiseEvent(over);
+
+        return over;
+    }
+
     private static void RightClick(Visual row, Visual window)
     {
         var at = Centre(row, window);
diff --git a/tests/DodoSSH.Client.App.Layout.Tests/ScreenLayoutTests.cs b/tests/DodoSSH.Client.App.Layout.Tests/ScreenLayoutTests.cs
index 535d46b..ae30074 100644
--- a/tests/DodoSSH.Client.App.Layout.Tests/ScreenLayoutTests.cs
+++ b/tests/DodoSSH.Client.App.Layout.Tests/ScreenLayoutTests.cs
@@ -325,22 +325,45 @@ public sealed class ScreenLayoutTests : IAsyncLifetime
         });
     }
 
+    /// <summary>
+    /// The grid is cards and nothing else, whatever the vault has been filed into.
+    /// </summary>
     /// <remarks>
-    /// Headings are items in the same list as the cards, drawn from a different template, and they span a
-    /// whole row of the wrap rather than sitting in the flow as another card. Measured with one group
-    /// folded, because a folded heading is the shape whose row is on screen without any of its hosts.
+    /// <para>
+    /// It used to hold the group headings too — a full-width fold-away bar between the cards for each group
+    /// — and in a wrap of cards that read as a dropdown somebody had left open. They are the phone's now.
+    /// This asserts the grid's contents rather than only measuring them, because a heading that came back
+    /// would lay out perfectly cleanly: the harness asks whether a control is inside the window, and a bar
+    /// that spans the width is as inside it as a card is.
+    /// </para>
+    /// <para>
+    /// Measured with every host filed, which is the shape that used to produce the most headings.
+    /// </para>
     /// </remarks>
     [Fact]
-    public async Task TheHostsScreenFitsWithGroupHeadingsInTheGrid()
+    public async Task TheHostsGridHoldsCardsAndNoGroupHeadings()
     {
         await SeedGroupsAsync(3);
 
-        vault.SidebarRows.OfType<SidebarGroupHeader>().Count()
-            .ShouldBe(3, "one heading per group, and no ungrouped heading while nothing is ungrouped");
+        foreach (var host in vault.Hosts.ToArray())
+        {
+            await vault.MoveHostToGroupCommand.ExecuteAsync(
+                new HostGroupMove(host, vault.Groups[0].EntityId));
+        }
 
-        vault.ToggleGroupCommand.Execute(vault.SidebarRows.OfType<SidebarGroupHeader>().First());
+        await OnTheHostsScreenAsync((screen, _) =>
+        {
+            var rows = screen.HostGrid
+                .GetVisualDescendants()
+                .OfType<ListBoxItem>()
+                .Select(item => item.DataContext)
+                .ToList();
 
-        await MeasureHostsAsync(faults => faults.ShouldBeEmpty("with three headings and one folded"));
+            rows.ShouldNotBeEmpty("the seed has to put hosts in the grid");
+            rows.ShouldAllBe(row => row is HostRowViewModel);
+        });
+
+        await MeasureHostsAsync(faults => faults.ShouldBeEmpty("with three groups and every host filed"));
     }
 
     /// <remarks>
diff --git a/tests/DodoSSH.Client.App.Tests/ShellFlowTests.cs b/tests/DodoSSH.Client.App.Tests/ShellFlowTests.cs
index 6f81f22..754b6ef 100644
--- a/tests/DodoSSH.Client.App.Tests/ShellFlowTests.cs
+++ b/tests/DodoSSH.Client.App.Tests/ShellFlowTests.cs
@@ -3368,9 +3368,9 @@ public sealed class ShellFlowTests : IAsyncLifetime
     }
 
     /// <remarks>
-    /// What dragging a row onto a heading does. It is the same write the editor makes — one field of the
-    /// host, pushed straight away — reached without opening a form, because filing thirty imported machines
-    /// through the editor is thirty rounds of open, pick, save.
+    /// What dragging a host card onto a group card does. It is the same write the editor makes — one field
+    /// of the host, pushed straight away — reached without opening a form, because filing thirty imported
+    /// machines through the editor is thirty rounds of open, pick, save.
     /// </remarks>
     [Fact]
     public async Task MovingAHostToAGroup_FilesItAndLeavesItSelected()
@@ -3389,15 +3389,21 @@ public sealed class ShellFlowTests : IAsyncLifetime
         vault.Hosts.Single().Host.GroupId.ShouldBe(group);
         vault.SelectedHost.ShouldNotBeNull().EntityId.ShouldBe(host.EntityId, "the reload replaces every row");
 
-        // Under the group's own heading now, which is the thing the drop was aiming at.
+        // Under the group's own heading now, which is what the phone's list draws.
         vault.SidebarRows.OfType<SidebarGroupHeader>()
             .Single(header => header.GroupId == group)
             .Count.ShouldBe(1);
 
-        // And back out again, which is what the ungrouped heading is a target for.
+        // And the name on the card, which is what the desktop's grid draws instead of that heading — the one
+        // thing on screen that changes where the host was dropped rather than where it came from.
+        vault.Hosts.Single().GroupLabel.ShouldBe("production");
+        vault.Hosts.Single().HasGroup.ShouldBeTrue();
+
+        // And back out again, which is what the host's own editor is for now that the drop has one target.
         await vault.MoveHostToGroupCommand.ExecuteAsync(new HostGroupMove(vault.Hosts.Single(), null));
 
         vault.Hosts.Single().Host.GroupId.ShouldBeNull();
+        vault.Hosts.Single().HasGroup.ShouldBeFalse("and the chip goes with it");
     }
 
     /// <remarks>
@@ -3454,9 +3460,13 @@ public sealed class ShellFlowTests : IAsyncLifetime
         vault.Groups.ShouldBeEmpty();
         vault.HasGroups.ShouldBeFalse();
 
-        // The host keeps the id, which is what makes this cheap; the sidebar is what resolves it to nothing.
+        // The host keeps the id, which is what makes this cheap; the list is what resolves it to nothing.
         vault.Hosts.Single().Host.GroupId.ShouldBe(groupId);
         vault.SidebarRows.ShouldAllBe(row => row is HostRowViewModel);
+
+        // The card says the same thing the phone's list does: nothing. An id nobody can name is drawn as no
+        // group rather than as a GUID on a chip.
+        vault.Hosts.Single().GroupLabel.ShouldBeEmpty();
     }
 
     /// <remarks>