diff --git a/crates/engine/src/cmd/scripts.rs b/crates/engine/src/cmd/scripts.rs
index 251531a07..7ad0d34c3 100644
--- a/crates/engine/src/cmd/scripts.rs
+++ b/crates/engine/src/cmd/scripts.rs
@@ -577,7 +577,7 @@ pub fn specs() -> Vec<CommandSpec> {
             "Mouse Event on Script Window Control",
             [],
             None,
-            "{window?, widget, type: mousedown | mouseup | mousemove | mouseover | mouseout | click (default), x?, y? (relative to the control; default its centre), button? (0 left, 1 middle, 2 right), detail? (click count), screenX?, screenY?, altKey?, ctrlKey?, metaKey?, shiftKey?} → the script's addEventListener listeners on the control and its containers receive a MouseEvent",
+            "{window?, widget, type: mousedown | mouseup | mousemove | mouseover | mouseout | click (default), x?, y? (relative to the control; default its centre), button? (0 left, 1 middle, 2 right), buttons? (held: 1 left, 2 right, 4 middle), detail? (click count), screenX?, screenY?, altKey?, ctrlKey?, metaKey?, shiftKey?} → the script's addEventListener listeners on the control and its containers receive a MouseEvent",
             always,
             scriptui::mouse
         ),
diff --git a/crates/engine/src/scriptui.rs b/crates/engine/src/scriptui.rs
index 082f0c861..1ad4b9a40 100644
--- a/crates/engine/src/scriptui.rs
+++ b/crates/engine/src/scriptui.rs
@@ -759,6 +759,7 @@ pub(crate) fn mouse(s: &mut Session, p: &Value) -> Result<Value> {
         "screenX": num("screenX", -FAR, FAR, 0.0),
         "screenY": num("screenY", -FAR, FAR, 0.0),
         "button": num("button", 0.0, 2.0, 0.0).round(),
+        "buttons": num("buttons", 0.0, 7.0, 0.0).round(),
         "detail": num("detail", 0.0, 1000.0, clicks).round(),
         "altKey": flag("altKey"),
         "ctrlKey": flag("ctrlKey"),
diff --git a/crates/script/src/scriptui.js b/crates/script/src/scriptui.js
index 4760d058b..178bd8be1 100644
--- a/crates/script/src/scriptui.js
+++ b/crates/script/src/scriptui.js
@@ -745,7 +745,8 @@ function __uiMouseWanted(c, inherited) {
 }
 
 // A ScriptUI MouseEvent. `v`: {x, y (relative to the target control), button (0 left, 1 middle,
-// 2 right), detail (click count), screenX, screenY, altKey, ctrlKey, metaKey, shiftKey}.
+// 2 right), buttons (held: 1 left, 2 right, 4 middle), detail (click count), screenX, screenY,
+// altKey, ctrlKey, metaKey, shiftKey}.
 function __uiMouseEvent(type, target, v) {
   var num = function (x, d) {
     x = Number(x);
@@ -765,6 +766,7 @@ function __uiMouseEvent(type, target, v) {
     timeStamp: new Date(),
     detail: num(v.detail, type === "mousemove" || type === "mouseover" || type === "mouseout" ? 0 : 1),
     button: num(v.button, 0),
+    buttons: num(v.buttons, 0),
     clientX: num(v.x, 0),
     clientY: num(v.y, 0),
     screenX: num(v.screenX, 0),
diff --git a/crates/ui-egui/src/panels/scriptui_view.rs b/crates/ui-egui/src/panels/scriptui_view.rs
index d12309b02..14460ed28 100644
--- a/crates/ui-egui/src/panels/scriptui_view.rs
+++ b/crates/ui-egui/src/panels/scriptui_view.rs
@@ -395,7 +395,11 @@ fn mouse_events(ui: &egui::Ui, origin: egui::Pos2, area: Rect, win: u32, root: &
         return;
     }
     let mut st: MouseTrack = ui.data(|d| d.get_temp(id)).unwrap_or_default();
-    let (latest, events, mods, time) = ui.input(|i| (i.pointer.latest_pos(), i.events.clone(), i.modifiers, i.time));
+    let (latest, events, mods, time, held) = ui.input(|i| {
+        let held = |b: egui::PointerButton, bit: u8| if i.pointer.button_down(b) { bit } else { 0 };
+        let held = held(egui::PointerButton::Primary, 1) | held(egui::PointerButton::Secondary, 2) | held(egui::PointerButton::Middle, 4);
+        (i.pointer.latest_pos(), i.events.clone(), i.modifiers, i.time, held)
+    });
     let ctx = ui.ctx();
     let layer = ui.layer_id();
     let target = |p: egui::Pos2| -> Option<&Widget> {
@@ -414,7 +418,7 @@ fn mouse_events(ui: &egui::Ui, origin: egui::Pos2, area: Rect, win: u32, root: &
             w.id,
             json!({
                 "type": ty, "x": p.x - at.x, "y": p.y - at.y, "screenX": p.x, "screenY": p.y,
-                "button": button, "detail": detail,
+                "button": button, "buttons": held, "detail": detail,
                 "altKey": mods.alt, "ctrlKey": mods.ctrl, "shiftKey": mods.shift, "metaKey": mods.mac_cmd,
             }),
         ));
@@ -431,10 +435,15 @@ fn mouse_events(ui: &egui::Ui, origin: egui::Pos2, area: Rect, win: u32, root: &
         }
         st.hover = now_id;
     }
-    if let Some((w, p)) = now
-        && st.at != Some(p)
-    {
-        send(w, "mousemove", p, 0, 0, acts);
+    // While a button is held, the control it was pressed on keeps getting the moves, inside or
+    // outside the window, as in After Effects (#2584).
+    let captured = st.down.and_then(|(c, _)| root.find(c));
+    if let Some(p) = latest.filter(|p| st.at != Some(*p)) {
+        match (captured, now) {
+            (Some(c), _) => send(c, "mousemove", p, 0, 0, acts),
+            (None, Some((w, _))) => send(w, "mousemove", p, 0, 0, acts),
+            (None, None) => {}
+        }
     }
     st.at = latest;
     // Presses and releases.
@@ -446,7 +455,9 @@ fn mouse_events(ui: &egui::Ui, origin: egui::Pos2, area: Rect, win: u32, root: &
             egui::PointerButton::Secondary => 2,
             _ => continue,
         };
-        let Some(w) = target(*pos) else {
+        // A release goes to the control the button was pressed on, wherever the pointer is.
+        let pressed_on = st.down.filter(|(_, db)| !*pressed && *db == b).and_then(|(c, _)| root.find(c));
+        let Some(w) = pressed_on.or_else(|| target(*pos)) else {
             if !pressed {
                 st.down = None;
             }
@@ -460,7 +471,8 @@ fn mouse_events(ui: &egui::Ui, origin: egui::Pos2, area: Rect, win: u32, root: &
             send(w, "mousedown", *pos, b, st.clicks, acts);
         } else {
             send(w, "mouseup", *pos, b, st.clicks, acts);
-            if st.down == Some((w.id, b)) && b == 0 && w.enabled && w.mouse.iter().any(|m| m == "click") {
+            let over = target(*pos).is_some_and(|t| t.id == w.id);
+            if over && st.down == Some((w.id, b)) && b == 0 && w.enabled && w.mouse.iter().any(|m| m == "click") {
                 // The click with the pointer's details, after mousedown / mouseup, in place of
                 // the plain click the control reported.
                 acts.retain(|a| !matches!(a, Act::Click(aw, ac) if *aw == win && *ac == w.id));
diff --git a/crates/ui-egui/tests/it/ui_scriptui.rs b/crates/ui-egui/tests/it/ui_scriptui.rs
index 938d1a827..09986f6d1 100644
--- a/crates/ui-egui/tests/it/ui_scriptui.rs
+++ b/crates/ui-egui/tests/it/ui_scriptui.rs
@@ -300,6 +300,47 @@ fn script_windows_send_mouse_events_to_listeners() {
     h.state_mut().session.execute("scriptui.close", json!({})).unwrap();
 }
 
+/// #2584: a drag that starts on a control keeps reaching it outside the script window (moves and
+/// the release), and `MouseEvent.buttons` tells a drag from a hover.
+#[test]
+fn a_drag_keeps_its_control_past_the_window_edge() {
+    let mut h = harness();
+    let code = r#"
+      var w = new Window("palette", "Drag");
+      var pad = w.add("group", undefined, undefined, { name: "pad" });
+      pad.preferredSize = [120, 80];
+      var log = w.add("statictext", undefined, "", { name: "log" });
+      log.preferredSize = [400, 20];
+      var seen = [];
+      var rec = function (e) { seen.push(e.type + (e.clientX < 0 ? " out" : " in") + " B" + e.buttons); log.text = seen.join("|"); };
+      pad.addEventListener("mousedown", rec);
+      pad.addEventListener("mousemove", rec);
+      pad.addEventListener("mouseup", rec);
+      w.show();
+    "#;
+    let r = h.state_mut().session.execute("script.run", json!({"code": code, "name": "drag.jsx"})).unwrap();
+    assert_eq!(r["ok"], true, "{r}");
+    h.run_steps(3);
+    let win = h.state().session.script_ui.windows[0].id;
+    let pad = rect(&h, &format!("scriptui.{win}.pad"));
+    let (from, to) = (pad.min + vec2(10.0, 20.0), pad.min + vec2(-300.0, 20.0));
+    h.input_mut().events.push(Event::PointerMoved(from));
+    h.run_steps(1);
+    h.input_mut().events.push(Event::PointerButton { pos: from, button: egui::PointerButton::Primary, pressed: true, modifiers: Default::default() });
+    h.run_steps(1);
+    for k in 1..=4 {
+        h.input_mut().events.push(Event::PointerMoved(from + (to - from) * (k as f32 / 4.0)));
+        h.run_steps(1);
+    }
+    h.input_mut().events.push(Event::PointerButton { pos: to, button: egui::PointerButton::Primary, pressed: false, modifiers: Default::default() });
+    h.run_steps(3);
+    let log = h.state().session.script_ui.windows[0].root.lookup(&json!("log")).cloned().unwrap().text;
+    assert!(log.starts_with("mousemove in B0|mousedown in B1|"), "a hover move has no button held: {log}");
+    assert!(log.contains("mousedown in B1|mousemove out B1"), "moves outside the window still arrive, with the button held: {log}");
+    assert!(log.ends_with("|mouseup out B0"), "the release outside reaches the control: {log}");
+    h.state_mut().session.execute("scriptui.close", json!({})).unwrap();
+}
+
 fn click_at(h: &mut Harness<'_, EffectcraftApp>, c: egui::Pos2) {
     h.input_mut().events.push(Event::PointerMoved(c));
     h.run_steps(1);