diff --git a/crates/ui-egui/src/panel_docking/peek.rs b/crates/ui-egui/src/panel_docking/peek.rs
index baf147f4fd..ed43b80e3d 100644
--- a/crates/ui-egui/src/panel_docking/peek.rs
+++ b/crates/ui-egui/src/panel_docking/peek.rs
@@ -41,6 +41,8 @@ struct Shown {
     edge: Edge,
     /// When the pointer left them; `None` while it is over them or has not moved since they showed.
     left_at: Option<f64>,
+    /// Whether a press, a modal dialog, a popup or a flyout held them open last frame.
+    held: bool,
 }
 
 /// The session's state of the panels shown from the edges.
@@ -102,9 +104,11 @@ pub(super) fn update(app: &mut VectorcraftApp, ctx: &egui::Context, area: egui::
         return None;
     }
     let (now, pointer, down, moved) = ctx.input(|i| {
-        // A release counts as moving away: a press may have held the panels while it left them.
-        let moved =
-            i.pointer.delta() != egui::Vec2::ZERO || i.pointer.any_released() || i.events.iter().any(|e| matches!(e, egui::Event::PointerGone));
+        // A release counts as moving away: a press may have held the panels while it left them. A
+        // pointer entering the window has no delta on its first frame, so the move event counts too.
+        let moved = i.pointer.delta() != egui::Vec2::ZERO
+            || i.pointer.any_released()
+            || i.events.iter().any(|e| matches!(e, egui::Event::PointerMoved(_) | egui::Event::PointerGone));
         (i.time, i.pointer.hover_pos(), i.pointer.any_down(), moved)
     });
     // A workspace switched to while panels show may dock none on that side.
@@ -123,11 +127,15 @@ pub(super) fn update(app: &mut VectorcraftApp, ctx: &egui::Context, area: egui::
                     Edge::Right => p.x > uncovered.right(),
                 }
         });
-        if over || down || blocked || flyout {
+        let held = down || blocked || flyout;
+        if over || held {
             shown.left_at = None;
-        } else if moved || pointer.is_none() {
+        } else if moved || shown.held {
+            // A hold that ends with the pointer away from them counts as moving away, as closing a
+            // popup or flyout with Escape does not move the pointer.
             shown.left_at.get_or_insert(now);
         }
+        shown.held = held;
         match shown.left_at {
             Some(left) if now - left >= GRACE => {
                 st.shown = None;
@@ -160,7 +168,7 @@ pub(super) fn update(app: &mut VectorcraftApp, ctx: &egui::Context, area: egui::
     };
     if now - since >= DELAY {
         st.resting = None;
-        st.shown = Some(Shown { edge, left_at: None });
+        st.shown = Some(Shown { edge, left_at: None, held: false });
         return Some(edge);
     }
     st.resting = Some((edge, since));
@@ -233,7 +241,7 @@ pub(super) fn command(app: &mut VectorcraftApp, params: &Value) -> Result<Value,
             }
             let st = &mut app.dock_rt.peek;
             st.resting = None;
-            st.shown = Some(Shown { edge, left_at: None });
+            st.shown = Some(Shown { edge, left_at: None, held: false });
             Ok(json!(edge.id()))
         }
         None => {
diff --git a/crates/ui-egui/src/panel_docking/tests.rs b/crates/ui-egui/src/panel_docking/tests.rs
index 2c95ff0e16..c78622458f 100644
--- a/crates/ui-egui/src/panel_docking/tests.rs
+++ b/crates/ui-egui/src/panel_docking/tests.rs
@@ -642,6 +642,45 @@ fn window_panels_peek_rejects_what_it_cannot_show_and_changes_nothing() {
     h.app.ui.screen_mode = 0;
 }
 
+#[test]
+fn panels_shown_by_window_panels_peek_stay_until_the_pointer_moves_or_leaves_the_window() {
+    let mut h = Harness::new();
+    let wide = hide_with_tab(&mut h);
+    assert_eq!(h.app.run("window.panels.peek", json!({"side": "right"})).unwrap(), json!("right"));
+    wait(&mut h, peek::GRACE * 2.0);
+    assert!(h.tab("properties").is_some(), "with no pointer movement, the panels stay");
+    assert_eq!(inspect(&h.app, &h.ctx)["peek"], json!("right"));
+    h.frame(vec![Event::PointerMoved(wide.center())]);
+    wait(&mut h, peek::GRACE * 2.0);
+    assert!(h.tab("properties").is_none(), "the pointer moved away from them, so they hide");
+    // The pointer leaving the window counts as moving away.
+    h.app.run("window.panels.peek", json!({"side": "right"})).unwrap();
+    wait(&mut h, peek::GRACE * 2.0);
+    assert!(h.tab("properties").is_some());
+    h.frame(vec![Event::PointerGone]);
+    wait(&mut h, peek::GRACE * 2.0);
+    assert!(h.tab("properties").is_none(), "the pointer left the window, so they hide");
+    assert_eq!(inspect(&h.app, &h.ctx)["peek"], Value::Null);
+}
+
+#[test]
+fn panels_held_by_a_flyout_hide_after_it_closes_with_the_pointer_still_away_from_them() {
+    let mut h = Harness::new();
+    let wide = hide_with_tab(&mut h);
+    // The pointer rests on the canvas, then outside the window, while a flyout holds the panels.
+    for away in [vec![Event::PointerMoved(wide.center())], vec![Event::PointerGone]] {
+        h.app.run("window.panels.peek", json!({"side": "right"})).unwrap();
+        h.app.ui.open_panel = Some("swatches".into());
+        h.frame(away);
+        wait(&mut h, peek::GRACE * 2.0);
+        assert!(h.tab("properties").is_some(), "an open flyout keeps them");
+        h.app.ui.open_panel = None;
+        wait(&mut h, peek::GRACE * 2.0);
+        assert!(h.tab("properties").is_none(), "the flyout closed with the pointer away from them, so they hide");
+        assert_eq!(inspect(&h.app, &h.ctx)["peek"], Value::Null);
+    }
+}
+
 #[test]
 fn edge_panels_are_the_docked_panels_on_each_side_of_the_canvas() {
     let layout = default_from(DockTab::ALL[0], &[], false, None, None);