diff --git a/crates/ui-egui/src/dialogs/mod.rs b/crates/ui-egui/src/dialogs/mod.rs
index dde768d5..8f049f8a 100644
--- a/crates/ui-egui/src/dialogs/mod.rs
+++ b/crates/ui-egui/src/dialogs/mod.rs
@@ -91,6 +91,10 @@ use crate::{VectorcraftApp, widgets};
 
 type DialogResult = Result<Value, String>;
 
+/// The shared dialog frame's inner margin, and the least room it leaves at the window's edges.
+const MARGIN: i8 = 22;
+const EDGE_GAP: f32 = 8.0;
+
 /// How a dialog draws and applies itself. Specs start from [`DialogSpec::FORM`] and override what
 /// differs.
 pub(crate) struct DialogSpec {
@@ -298,12 +302,12 @@ pub fn show(app: &mut VectorcraftApp, ctx: &egui::Context) {
         .resizable(false)
         .title_bar(false)
         .anchor(egui::Align2::CENTER_CENTER, [0.0, -40.0])
-        .frame(egui::Frame::window(&ctx.global_style()).fill(t.panel).inner_margin(egui::Margin::same(22)))
+        .frame(egui::Frame::window(&ctx.global_style()).fill(t.panel).inner_margin(egui::Margin::same(MARGIN)))
         .show(ctx, |ui| {
-            ui.set_min_width(spec.min_width);
-            if let Some(w) = spec.max_width {
-                ui.set_max_width(w);
-            }
+            // Never wider than the window (a large UI scale in a small window): the text wraps.
+            let room = (ctx.content_rect().width() - 2.0 * (f32::from(MARGIN) + EDGE_GAP)).max(EDGE_GAP);
+            ui.set_min_width(spec.min_width.min(room));
+            ui.set_max_width(spec.max_width.map_or(room, |w| w.min(room)));
             ui.label(egui::RichText::new(heading.as_str()).font(theme::semibold(16.0)).color(t.text));
             ui.add_space(12.0);
             cancel = (spec.body)(app, ui, &mut d);
@@ -383,3 +387,6 @@ mod tests_print_presets;
 
 #[cfg(test)]
 mod tests_print_advanced;
+
+#[cfg(test)]
+mod tests_scale;
diff --git a/crates/ui-egui/src/dialogs/tests_scale.rs b/crates/ui-egui/src/dialogs/tests_scale.rs
new file mode 100644
index 00000000..efe9bdc1
--- /dev/null
+++ b/crates/ui-egui/src/dialogs/tests_scale.rs
@@ -0,0 +1,41 @@
+//! The shared dialog frame at every UI scale (Preferences → User Interface → UI Scaling zooms the
+//! whole interface, so a window holds fewer points).
+
+use serde_json::json;
+use vectorcraft_engine::Session;
+
+use super::*;
+
+/// The save prompt's rect after a few frames in a window of `physical` pixels at UI scale `zoom`.
+fn prompt(app: &mut VectorcraftApp, ctx: &egui::Context, physical: egui::Vec2, zoom: f32) -> (egui::Rect, egui::Rect) {
+    ctx.set_zoom_factor(zoom);
+    let screen = egui::Rect::from_min_size(egui::Pos2::ZERO, physical / zoom);
+    for _ in 0..10 {
+        let input = egui::RawInput { screen_rect: Some(screen), ..Default::default() };
+        ctx.run_ui(input, |ui| show(app, ui.ctx())).textures_delta.clear();
+    }
+    let rect = ctx.memory(|m| m.area_rect(egui::Id::new(("dialog", crate::unsaved::KIND)))).unwrap();
+    (rect, screen)
+}
+
+#[test]
+fn the_save_prompt_fits_its_content_and_the_window_at_every_ui_scale() {
+    let mut app = VectorcraftApp::new(Session::new(), Default::default());
+    app.run("file.new", json!({"width": 200, "height": 200})).unwrap();
+    let ctx = egui::Context::default();
+    theme::install_fonts(&ctx);
+    theme::apply(&ctx, Default::default());
+    for name in ["Untitled-1", "Quarterly campaign poster, final revision with the printer's notes"] {
+        app.ui.dialog = Some(Dialog::new(crate::unsaved::KIND, json!({"index": 0, "name": name, "then": "close"})));
+        // Scaled up and down while the prompt is open, in a full-size and in the smallest window.
+        for (w, h, zoom) in
+            [(1440.0, 900.0, 1.0), (1440.0, 900.0, 2.0), (1440.0, 900.0, 1.5), (800.0, 500.0, 2.0), (800.0, 500.0, 1.0), (1440.0, 900.0, 0.75)]
+        {
+            let (rect, screen) = prompt(&mut app, &ctx, egui::vec2(w, h), zoom);
+            let at = format!("{name}: {w} × {h} px at {zoom}×: {rect:?} in {screen:?}");
+            assert!(screen.contains_rect(rect), "inside the window, {at}");
+            // As tall as its text and buttons (no empty band around the buttons).
+            assert!(rect.height() < 200.0, "{at}");
+        }
+    }
+}