diff --git a/crates/ui-egui/src/dialogs.rs b/crates/ui-egui/src/dialogs.rs
index dd8f83fb..47305032 100644
--- a/crates/ui-egui/src/dialogs.rs
+++ b/crates/ui-egui/src/dialogs.rs
@@ -1935,7 +1935,10 @@ fn picked_side(app: &SolveApp, d: &Dialog, first: &Sel) -> Option<usize> {
 /// Sketch Palette keeps the right there, and the dialog takes the left so both stay on screen.
 pub fn show(app: &mut SolveApp, ctx: &egui::Context) {
     app.viewport.dialog_rect = None;
-    let Some(mut d) = app.dialog.take() else { return };
+    let Some(mut d) = app.dialog.take() else {
+        crate::frame::reset_dock_offset(ctx);
+        return;
+    };
     // Edit Text lasts as long as its text: other design changes leave it open.
     if let Kind::Text(k) = &mut d.kind
         && !crate::sketch_text::refresh(app, k)
@@ -1979,7 +1982,11 @@ pub fn show(app: &mut SolveApp, ctx: &egui::Context) {
     } else {
         crate::frame::Side::Right
     };
-    let anchor = egui::pos2(side.anchor_x(vp), top);
+    // Dragged by its title band, the dialog keeps that offset from its docked place while it
+    // is open (#1335), kept inside the viewport.
+    let moved = crate::frame::dock_offset(ctx, title(&d.kind));
+    let docked = egui::pos2(side.anchor_x(vp), top);
+    let anchor = crate::frame::offset_anchor(docked, moved, vp, side);
     let mut keep = true;
     let mut ok = false;
     let mut applied = false;
@@ -2020,7 +2027,11 @@ pub fn show(app: &mut SolveApp, ctx: &egui::Context) {
         ui.set_max_width(if wide { DIALOG_WIDE_MAX_W } else { DIALOG_MAX_W } - margin);
         // Rows that end at the right edge line up with last frame's content width.
         let total = crate::frame::content_width(ui, wkey, min_w);
-        // Header: "−" folds the dialog, the command name, "»" at the right, on the title band.
+        // Header: "−" folds the dialog, the command name, "»" at the right, on the title band,
+        // which also moves the dialog.
+        let band_top = ui.cursor().min;
+        let band = egui::Rect::from_min_size(band_top, vec2(total, ui.spacing().interact_size.y + 2.0));
+        crate::frame::drag_dock(ui, band, title(&d.kind), moved, anchor - docked);
         crate::frame::heading(ui, crate::frame::Level::Title, total, |ui| {
             let total = total - 2.0 * crate::frame::HEADING_MARGIN;
             let fold = if d.collapsed { "+" } else { "−" };
@@ -2031,7 +2042,8 @@ pub fn show(app: &mut SolveApp, ctx: &egui::Context) {
             {
                 d.collapsed = !d.collapsed;
             }
-            ui.label(RichText::new(heading.as_str()).strong().size(12.5));
+            // Not selectable: a drag on the title moves the dialog.
+            ui.add(egui::Label::new(RichText::new(heading.as_str()).strong().size(12.5)).selectable(false));
             let chevron_width = ui.spacing().interact_size.x;
             crate::frame::right_aligned(ui, total, chevron_width, |ui| {
                 let chevron = if d.collapsed { "«" } else { "»" };
diff --git a/crates/ui-egui/src/frame.rs b/crates/ui-egui/src/frame.rs
index 6e7dcff2..87f4d838 100644
--- a/crates/ui-egui/src/frame.rs
+++ b/crates/ui-egui/src/frame.rs
@@ -92,6 +92,63 @@ pub fn docked_on<'a>(title: impl Into<WidgetText>, id: egui::Id, anchor: Pos2, m
         .max_height(max_height.max(120.0))
 }
 
+/// How far the open docked dialog titled `title` was dragged from its docked place (#1335);
+/// zero for a dialog that was not dragged, or once another dialog opens.
+pub fn dock_offset(ctx: &egui::Context, title: &str) -> egui::Vec2 {
+    ctx.data(|d| d.get_temp::<(String, egui::Vec2)>(egui::Id::new("sc_dock_offset")))
+        .filter(|(t, _)| t == title)
+        .map(|(_, v)| v)
+        .unwrap_or(egui::Vec2::ZERO)
+}
+
+/// Forget a dragged dialog's place (it closed): the next one opens docked.
+pub fn reset_dock_offset(ctx: &egui::Context) {
+    ctx.data_mut(|d| d.remove::<(String, egui::Vec2)>(egui::Id::new("sc_dock_offset")));
+}
+
+/// A docked dialog's anchor moved by `offset`, kept so its docked corner stays in `vp` with
+/// room for its title band.
+pub fn offset_anchor(docked: Pos2, offset: egui::Vec2, vp: egui::Rect, side: Side) -> Pos2 {
+    let p = docked + offset;
+    let (lo, hi) = match side {
+        Side::Right => (vp.left() + DIALOG_MIN_W, vp.right()),
+        Side::Left => (vp.left(), vp.right() - DIALOG_MIN_W),
+    };
+    let x = if lo <= hi { p.x.clamp(lo, hi) } else { docked.x };
+    let y = if vp.top() <= vp.bottom() - 40.0 { p.y.clamp(vp.top(), vp.bottom() - 40.0) } else { docked.y };
+    egui::pos2(x, y)
+}
+
+/// Let `band` (a docked dialog's title band) drag the dialog: the drag adds to its offset
+/// `moved` (as last frame left it; `applied` of it is where the dialog is now, after keeping
+/// it on screen). Called before the band's buttons are added, so they keep their clicks.
+pub fn drag_dock(ui: &Ui, band: egui::Rect, title: &str, moved: egui::Vec2, applied: egui::Vec2) {
+    let response = ui.interact(band, ui.id().with("sc_dock_drag"), egui::Sense::drag());
+    crate::scenario::publish_handle("dialog:title", band.center());
+    // The drag runs from where the press started, so no movement is lost while egui decides
+    // it is a drag, nor on the frame it ends.
+    let base = egui::Id::new("sc_dock_drag_base");
+    if response.drag_started()
+        && let Some(origin) = ui.input(|i| i.pointer.press_origin())
+    {
+        ui.ctx().data_mut(|d| d.insert_temp(base, (applied, origin)));
+    }
+    if response.dragged() || response.drag_stopped() {
+        ui.ctx().set_cursor_icon(egui::CursorIcon::Grabbing);
+        let start = ui.ctx().data(|d| d.get_temp::<(egui::Vec2, Pos2)>(base));
+        let to = match (start, ui.input(|i| i.pointer.latest_pos())) {
+            (Some((start, from)), Some(now)) => start + (now - from),
+            _ => applied + response.drag_delta(),
+        };
+        ui.ctx().data_mut(|d| d.insert_temp(egui::Id::new("sc_dock_offset"), (title.to_string(), to)));
+    } else if response.hovered() {
+        ui.ctx().set_cursor_icon(egui::CursorIcon::Grab);
+    } else if moved != applied {
+        // Kept on screen: remember where it is, not where it was dragged off to.
+        ui.ctx().data_mut(|d| d.insert_temp(egui::Id::new("sc_dock_offset"), (title.to_string(), applied)));
+    }
+}
+
 /// A floating window, centred on the screen unless the caller places it, shrink-wrapped to its
 /// content up to its width limit.
 pub fn window<'a>(ctx: &egui::Context, title: impl Into<WidgetText>, width: Width) -> egui::Window<'a> {
@@ -229,6 +286,43 @@ mod tests {
             assert!(h.app.dialog.is_none());
         }
     }
+    /// #1335: a dialog keeps its size while its Select chip is hovered, and its title band
+    /// drags it; it opens docked again after it closes.
+    #[test]
+    fn a_docked_dialog_keeps_its_size_under_the_pointer_and_moves_by_its_title() {
+        use crate::scenario::Harness;
+        use serde_json::json;
+        let mut h = Harness::new();
+        h.call("ui.resize", json!({"width":1400.0,"height":900.0}));
+        h.step(&json!({"start":"sketch.create"})).unwrap();
+        h.frames(6);
+        let rest = h.app.viewport.dialog_rect.unwrap();
+        let chip = crate::scenario::handle_at("dialog:Plane").unwrap();
+        h.call("ui.move", json!({"x": chip.x, "y": chip.y}));
+        h.frames(6);
+        let hovered = h.app.viewport.dialog_rect.unwrap();
+        assert!((hovered.size() - rest.size()).length() < 0.01, "hovering resized the dialog: {rest:?} -> {hovered:?}");
+        // Dragged by its title text.
+        let title = h.widget("CREATE SKETCH").map(|[x, y]| egui::pos2(x as f32, y as f32)).unwrap();
+        h.call("ui.drag", json!({"x0": title.x, "y0": title.y, "x1": title.x - 300.0, "y1": title.y + 120.0, "steps": 8}));
+        h.frames(4);
+        let moved = h.app.viewport.dialog_rect.unwrap();
+        assert!((moved.min - rest.min - egui::vec2(-300.0, 120.0)).length() < 2.0, "{rest:?} -> {moved:?}");
+        assert!(h.app.dialog.is_some(), "dragging the title keeps the dialog open");
+        // Dragged far off, it stays on screen.
+        let title = crate::scenario::handle_at("dialog:title").unwrap();
+        h.call("ui.drag", json!({"x0": title.x, "y0": title.y, "x1": title.x + 3000.0, "y1": title.y + 3000.0, "steps": 8}));
+        h.frames(4);
+        let viewport = h.app.viewport.rect.unwrap();
+        assert!(viewport.contains(h.app.viewport.dialog_rect.unwrap().min));
+        h.step(&json!({"key":"Escape"})).unwrap();
+        h.frames(2);
+        assert!(h.app.dialog.is_none());
+        h.step(&json!({"start":"sketch.create"})).unwrap();
+        h.frames(6);
+        assert!((h.app.viewport.dialog_rect.unwrap().min - rest.min).length() < 0.01, "a new dialog opens docked");
+    }
+
     /// Windows are made in this file only, so none can skip the width limits.
     #[test]
     fn windows_come_from_the_frame_helper() {