diff --git a/gnome-shell-extension/ai-control-popup@local/extension.js b/gnome-shell-extension/ai-control-popup@local/extension.js
index 295e18a..1762663 100644
--- a/gnome-shell-extension/ai-control-popup@local/extension.js
+++ b/gnome-shell-extension/ai-control-popup@local/extension.js
@@ -79,6 +79,7 @@ export default class AiControlPopupExtension extends Extension {
     const win = this._findWindow();
     if (win && win.showing_on_its_workspace()) {
       this._call('Hide');
+      this._disconnectOutsideClick();
       return;
     }
     // Fenster unsichtbar halten, bis es am Platz sitzt (kein Sprung Mitte->Tray).
@@ -86,6 +87,37 @@ export default class AiControlPopupExtension extends Extension {
     if (actor) actor.opacity = 0;
     this._call('Show');
     this._positionWhenReady();
+    this._connectOutsideClick();
+  }
+
+  // Klick auf leere Desktop-Fläche oder Shell-Chrome wechselt den Fensterfokus
+  // nicht — der Blur-Pfad der App greift dort nicht. Solche Klicks landen im
+  // Shell-Stage: solange das Popup offen ist, hier abgreifen und Hide relayen.
+  _connectOutsideClick() {
+    if (this._clickId) return;
+    this._clickId = global.stage.connect('captured-event', (_stage, event) => {
+      if (event.type() !== Clutter.EventType.BUTTON_PRESS) return Clutter.EVENT_PROPAGATE;
+      const win = this._findWindow();
+      if (!win || !win.showing_on_its_workspace()) {
+        this._disconnectOutsideClick();
+        return Clutter.EVENT_PROPAGATE;
+      }
+      const [x, y] = event.get_coords();
+      // Panel-Button toggelt selbst; Klicks ins Popup erreichen den Stage nicht.
+      const [bx, by] = this._button.get_transformed_position();
+      if (x >= bx && x < bx + this._button.width && y >= by && y < by + this._button.height) {
+        return Clutter.EVENT_PROPAGATE;
+      }
+      this._call('Hide');
+      this._disconnectOutsideClick();
+      return Clutter.EVENT_PROPAGATE;
+    });
+  }
+
+  _disconnectOutsideClick() {
+    if (!this._clickId) return;
+    global.stage.disconnect(this._clickId);
+    this._clickId = 0;
   }
 
   _call(method) {
@@ -186,6 +218,7 @@ export default class AiControlPopupExtension extends Extension {
       global.window_manager.disconnect(this._mapId);
       this._mapId = 0;
     }
+    this._disconnectOutsideClick();
     this._removeButton();
     this._proxy = null;
   }