diff --git a/apps/soundcraft/src/main.rs b/apps/soundcraft/src/main.rs
index 7e3b989..61f20bd 100644
--- a/apps/soundcraft/src/main.rs
+++ b/apps/soundcraft/src/main.rs
@@ -49,6 +49,13 @@ impl eframe::App for App {
         if self.0.quit_requested {
             ctx.send_viewport_cmd(egui::ViewportCommand::Close);
         }
+        soundcraft_ui_egui::fit_window_to_screen(ctx);
+        let (inner, maximized) = ctx.input(|i| (i.viewport().inner_rect, i.viewport().maximized.unwrap_or(false)));
+        self.0.ui.window_maximized = maximized;
+        if let Some(r) = inner.filter(|_| !maximized) {
+            self.0.ui.window_size = (r.size() * ctx.zoom_factor()).round().into();
+        }
+        self.0.ui.ui_scale = self.0.extra.ui_scale;
         // With the system menu bar there is no egui bar showing the window and dirty state, so the
         // title carries them; elsewhere the egui menu bar already does.
         let title = if self.0.native_menu_bar {
@@ -216,10 +223,12 @@ fn main() -> eframe::Result {
     }
 
     let engine = if demo { soundcraft_engine::demo::demo_engine() } else { Engine::default() };
+    let prefs = load_prefs().unwrap_or_default();
     let mut options = eframe::NativeOptions {
         viewport: egui::ViewportBuilder::default()
             .with_title("SoundCraft")
-            .with_inner_size([1600.0, 1000.0])
+            .with_inner_size(sane_window_size(prefs.window_size))
+            .with_maximized(prefs.window_maximized)
             .with_min_inner_size([960.0, 600.0])
             .with_drag_and_drop(true)
             .with_app_id("ai.storyteller.soundcraft"),
@@ -239,9 +248,8 @@ fn main() -> eframe::Result {
             let mut app = SoundApp::new(engine, player, services());
             app.autosave_dir = prefs_path().and_then(|p| p.parent().map(|d| d.join("Autosave")));
             app.preset_dir = prefs_path().and_then(|p| p.parent().map(|d| d.join("Presets")));
-            if let Some(ui) = load_prefs() {
-                app.ui = ui;
-            }
+            app.extra.ui_scale = prefs.ui_scale;
+            app.ui = prefs;
             if let Some(port) = control_port {
                 let rx = control_server::start(port, cc.egui_ctx.clone());
                 app = app.with_control(rx);
@@ -270,3 +278,8 @@ fn main() -> eframe::Result {
         }),
     )
 }
+
+/// A saved window size, or the default when the prefs file holds nonsense (NaN, negative, tiny).
+fn sane_window_size([w, h]: [f32; 2]) -> [f32; 2] {
+    if w.is_finite() && h.is_finite() && w >= 960.0 && h >= 600.0 { [w.min(16_384.0), h.min(16_384.0)] } else { [1600.0, 1000.0] }
+}
diff --git a/crates/ui-egui/src/lib.rs b/crates/ui-egui/src/lib.rs
index 8103a09..305ff2e 100644
--- a/crates/ui-egui/src/lib.rs
+++ b/crates/ui-egui/src/lib.rs
@@ -101,6 +101,11 @@ pub struct UiState {
     pub configurations: Vec<(String, Value)>,
     /// Appearance (`ui.theme`): dark by default, light or follow the system on request.
     pub theme: theme::ThemeMode,
+    /// The main window's size (logical points) and maximized state, and the interface scale, as
+    /// the desktop app last saw them; it restores them at launch.
+    pub window_size: [f32; 2],
+    pub window_maximized: bool,
+    pub ui_scale: f32,
 }
 
 impl Default for UiState {
@@ -153,6 +158,9 @@ impl Default for UiState {
             workspace_dir: String::new(),
             configurations: Vec::new(),
             theme: theme::ThemeMode::Dark,
+            window_size: [1600.0, 1000.0],
+            window_maximized: false,
+            ui_scale: 1.0,
         }
     }
 }
@@ -170,6 +178,15 @@ pub fn preset_folder_name(plugin: &str) -> String {
     plugin.chars().map(|c| if c.is_ascii_alphanumeric() || c == '.' || c == '-' || c == '_' { c } else { '_' }).collect()
 }
 
+/// On the first frame, maximizes a window too big for the screen it opened on (sized on a larger
+/// monitor) instead of letting it run off the edge; its saved size is kept for that monitor.
+pub fn fit_window_to_screen(ctx: &egui::Context) {
+    let (inner, monitor) = ctx.input(|i| (i.viewport().inner_rect, i.viewport().monitor_size));
+    if ctx.cumulative_pass_nr() == 0 && inner.zip(monitor).is_some_and(|(r, m)| (r.size() - m).max_elem() > 0.0) {
+        ctx.send_viewport_cmd(egui::ViewportCommand::Maximized(true));
+    }
+}
+
 /// Drag-and-drop payload: an audio file (source id) dragged from the Clip List.
 #[derive(Debug, Clone, Copy)]
 pub struct DragSource(pub u64);
@@ -1023,6 +1040,35 @@ mod tests {
         assert!(automation_step_due(0, 1_000_000, 960));
     }
 
+    #[test]
+    fn preferences_saved_before_the_window_was_remembered_keep_full_scale() {
+        let ui: super::UiState = serde_json::from_value(json!({"show_transport": true})).unwrap();
+        assert_eq!((ui.window_size, ui.window_maximized, ui.ui_scale), ([1600.0, 1000.0], false, 1.0));
+    }
+
+    #[test]
+    fn a_window_bigger_than_its_screen_opens_maximized() {
+        let maximizes = |w: f32, frames: usize| {
+            let ctx = egui::Context::default();
+            let info = egui::ViewportInfo {
+                inner_rect: Some(egui::Rect::from_min_size(egui::Pos2::ZERO, egui::vec2(w, 1000.0))),
+                monitor_size: Some(egui::vec2(1728.0, 1117.0)),
+                ..Default::default()
+            };
+            let mut maximized = false;
+            for _ in 0..frames {
+                let raw = egui::RawInput { viewports: [(egui::ViewportId::ROOT, info.clone())].into_iter().collect(), ..Default::default() };
+                let mut out = ctx.run_ui(raw, |ui| super::fit_window_to_screen(ui.ctx()));
+                out.textures_delta.clear();
+                maximized = out.viewport_output[&egui::ViewportId::ROOT].commands.contains(&egui::ViewportCommand::Maximized(true));
+            }
+            maximized
+        };
+        assert!(maximizes(2400.0, 1));
+        assert!(!maximizes(1600.0, 1));
+        assert!(!maximizes(2400.0, 2));
+    }
+
     #[test]
     fn ordinary_play_after_stop_is_full_speed() {
         use serde_json::json;
diff --git a/crates/ui-egui/src/panels.rs b/crates/ui-egui/src/panels.rs
index 153c983..5522169 100644
--- a/crates/ui-egui/src/panels.rs
+++ b/crates/ui-egui/src/panels.rs
@@ -412,44 +412,46 @@ fn plugin_windows(app: &mut SoundApp, ctx: &egui::Context) {
                 if info.id == "eq_7band" || info.id == "eq_1band" {
                     eq_curve(ui, info.id, &ins);
                 }
-                egui::Grid::new(("pg", tid.0, slot)).num_columns(3).show(ui, |ui| {
-                    for p in info.params {
-                        let v = ins.params.get(p.id).copied().unwrap_or(p.default);
-                        ui.label(p.name);
-                        let mut x = v;
-                        let resp = if !p.choices.is_empty() {
-                            let mut idx = x.round().max(0.0) as usize;
-                            let r = egui::ComboBox::from_id_salt(("pc", tid.0, slot, p.id))
-                                .selected_text(p.choices.get(idx).copied().unwrap_or("?"))
-                                .show_ui(ui, |ui| {
-                                    for (i, c) in p.choices.iter().enumerate() {
-                                        ui.selectable_value(&mut idx, i, *c);
-                                    }
-                                });
-                            x = idx as f32;
-                            r.response
-                        } else {
-                            let mut sl = egui::Slider::new(&mut x, p.min..=p.max).show_value(false);
-                            if p.taper == soundcraft_dsp::Taper::Log && p.min > 0.0 {
-                                sl = sl.logarithmic(true);
-                            }
-                            ui.add(sl)
-                        };
-                        if (x - v).abs() > f32::EPSILON {
-                            let _ = app.engine.execute_merged(
-                                "mix.insert_param",
-                                &json!({"track": tid.0, "slot": slot, "param": p.id, "value": x}),
-                                &format!("param:{}:{slot}:{}", tid.0, p.id),
-                            );
-                            if let Some(pl) = &app.player {
-                                // Keep the plugin's own editor in step.
-                                pl.editor_set_param(tid, slot, p.id, x);
+                egui::ScrollArea::vertical().show(ui, |ui| {
+                    egui::Grid::new(("pg", tid.0, slot)).num_columns(3).show(ui, |ui| {
+                        for p in info.params {
+                            let v = ins.params.get(p.id).copied().unwrap_or(p.default);
+                            ui.label(p.name);
+                            let mut x = v;
+                            let resp = if !p.choices.is_empty() {
+                                let mut idx = x.round().max(0.0) as usize;
+                                let r = egui::ComboBox::from_id_salt(("pc", tid.0, slot, p.id))
+                                    .selected_text(p.choices.get(idx).copied().unwrap_or("?"))
+                                    .show_ui(ui, |ui| {
+                                        for (i, c) in p.choices.iter().enumerate() {
+                                            ui.selectable_value(&mut idx, i, *c);
+                                        }
+                                    });
+                                x = idx as f32;
+                                r.response
+                            } else {
+                                let mut sl = egui::Slider::new(&mut x, p.min..=p.max).show_value(false);
+                                if p.taper == soundcraft_dsp::Taper::Log && p.min > 0.0 {
+                                    sl = sl.logarithmic(true);
+                                }
+                                ui.add(sl)
+                            };
+                            if (x - v).abs() > f32::EPSILON {
+                                let _ = app.engine.execute_merged(
+                                    "mix.insert_param",
+                                    &json!({"track": tid.0, "slot": slot, "param": p.id, "value": x}),
+                                    &format!("param:{}:{slot}:{}", tid.0, p.id),
+                                );
+                                if let Some(pl) = &app.player {
+                                    // Keep the plugin's own editor in step.
+                                    pl.editor_set_param(tid, slot, p.id, x);
+                                }
                             }
+                            let _ = resp;
+                            ui.label(egui::RichText::new(p.format(x)).font(mono(11.0)));
+                            ui.end_row();
                         }
-                        let _ = resp;
-                        ui.label(egui::RichText::new(p.format(x)).font(mono(11.0)));
-                        ui.end_row();
-                    }
+                    });
                 });
             });
         if open {
diff --git a/crates/ui-egui/tests/plugin_window.rs b/crates/ui-egui/tests/plugin_window.rs
new file mode 100644
index 0000000..2387033
--- /dev/null
+++ b/crates/ui-egui/tests/plugin_window.rs
@@ -0,0 +1,19 @@
+use egui_kittest::Harness;
+use soundcraft_ui_egui::{Services, SoundApp};
+
+#[test]
+fn a_long_plugin_window_stays_on_a_short_screen() {
+    let mut app = SoundApp::new(soundcraft_engine::demo::demo_engine(), None, Services::default());
+    let kick = app.engine.session().track_by_name("Kick").unwrap().id;
+    app.ui.plugin_windows = vec![(kick, 0)];
+    let mut h = Harness::builder().with_size(egui::vec2(1200.0, 500.0)).build_ui_state(
+        |ui, app: &mut SoundApp| {
+            app.logic(&ui.ctx().clone());
+            app.ui(ui);
+        },
+        app,
+    );
+    h.run_steps(4);
+    let window = h.ctx.memory(|m| m.area_rect(egui::Id::new(("plugin", kick.0, 0usize)))).unwrap();
+    assert!(window.bottom() <= 500.0, "{window:?}");
+}