diff --git a/src/compositor/compositor.c b/src/compositor/compositor.c
index 0fd6d6789..8982bbd08 100644
--- a/src/compositor/compositor.c
+++ b/src/compositor/compositor.c
@@ -971,24 +971,22 @@ maybe_spoof_event_as_stage_event (MetaCompScreen *info,
       event->xcookie.extension == display->xinput_opcode)
     {
       XIEvent *input_event = (XIEvent *) event->xcookie.data;
+      XIDeviceEvent *device_event = ((XIDeviceEvent *) input_event);
 
       switch (input_event->evtype)
         {
         case XI_Motion:
         case XI_ButtonPress:
         case XI_ButtonRelease:
-        case XI_KeyPress:
-        case XI_KeyRelease:
-          {
-            XIDeviceEvent *device_event = ((XIDeviceEvent *) input_event);
-
             /* If this is a GTK+ widget, like a window menu, let GTK+ handle
              * it as-is without mangling. */
             if (meta_ui_window_is_widget (info->screen->ui, device_event->event))
               break;
 
+            /* fall through */
+        case XI_KeyPress:
+        case XI_KeyRelease:
             device_event->event = clutter_x11_get_stage_window (CLUTTER_STAGE (info->stage));
-          }
           break;
         default:
           break;
@@ -1008,6 +1006,12 @@ meta_compositor_process_event (MetaCompositor *compositor,
                                XEvent         *event,
                                MetaWindow     *window)
 {
+  MetaDisplay *display = compositor->display;
+  MetaScreen *screen = display->screens->data;
+  MetaCompScreen *info;
+
+  info = meta_screen_get_compositor_data (screen);
+
   if (compositor->modal_plugin && is_grabbed_event (compositor->display, event))
     {
       _meta_plugin_xevent_filter (compositor->modal_plugin, event);
@@ -1017,43 +1021,12 @@ meta_compositor_process_event (MetaCompositor *compositor,
       return TRUE;
     }
 
-  if (window)
+  maybe_spoof_event_as_stage_event (info, event);
+
+  if (meta_plugin_manager_xevent_filter (info->plugin_mgr, event))
     {
-      MetaCompScreen *info;
-      MetaScreen     *screen;
-
-      screen = meta_window_get_screen (window);
-      info = meta_screen_get_compositor_data (screen);
-
-      if (meta_plugin_manager_xevent_filter (info->plugin_mgr, event))
-	{
-	  DEBUG_TRACE ("meta_compositor_process_event (filtered,window==NULL)\n");
-	  return TRUE;
-	}
-    }
-  else
-    {
-      GSList *l;
-
-      l = meta_display_get_screens (compositor->display);
-
-      while (l)
-	{
-	  MetaScreen     *screen = l->data;
-	  MetaCompScreen *info;
-
-	  info = meta_screen_get_compositor_data (screen);
-
-          maybe_spoof_event_as_stage_event (info, event);
-
-	  if (meta_plugin_manager_xevent_filter (info->plugin_mgr, event))
-	    {
-	      DEBUG_TRACE ("meta_compositor_process_event (filtered,window==NULL)\n");
-	      return TRUE;
-	    }
-
-	  l = l->next;
-	}
+      DEBUG_TRACE ("meta_compositor_process_event (filtered,window==NULL)\n");
+      return TRUE;
     }
 
   if (!meta_is_wayland_compositor () &&
diff --git a/src/core/keybindings.c b/src/core/keybindings.c
index db2db7687..bf33587df 100644
--- a/src/core/keybindings.c
+++ b/src/core/keybindings.c
@@ -1842,8 +1842,7 @@ process_event (MetaKeyBinding       *bindings,
                MetaDisplay          *display,
                MetaScreen           *screen,
                MetaWindow           *window,
-               ClutterKeyEvent      *event,
-               gboolean              on_window)
+               ClutterKeyEvent      *event)
 {
   int i;
 
@@ -1859,7 +1858,7 @@ process_event (MetaKeyBinding       *bindings,
     {
       MetaKeyHandler *handler = bindings[i].handler;
 
-      if ((!on_window && handler->flags & META_KEY_BINDING_PER_WINDOW) ||
+      if ((!window && handler->flags & META_KEY_BINDING_PER_WINDOW) ||
           (event->keyval != bindings[i].keysym) ||
           (event->modifier_state != bindings[i].mask) ||
           meta_compositor_filter_keybinding (display->compositor, screen, &bindings[i]))
@@ -1891,7 +1890,8 @@ process_event (MetaKeyBinding       *bindings,
 static gboolean
 process_overlay_key (MetaDisplay *display,
                      MetaScreen *screen,
-                     ClutterKeyEvent *event)
+                     ClutterKeyEvent *event,
+                     MetaWindow *window)
 {
   if (display->overlay_key_only_pressed)
     {
@@ -1913,8 +1913,7 @@ process_overlay_key (MetaDisplay *display,
            */
           if (process_event (display->key_bindings,
                              display->n_key_bindings,
-                             display, screen, NULL, event,
-                             FALSE))
+                             display, screen, window, event))
             {
               /* As normally, after we've handled a global key
                * binding, we unfreeze the keyboard but keep the grab
@@ -2056,7 +2055,7 @@ meta_display_process_key_event (MetaDisplay     *display,
   all_keys_grabbed = window ? window->all_keys_grabbed : screen->all_keys_grabbed;
   if (!all_keys_grabbed)
     {
-      handled = process_overlay_key (display, screen, event);
+      handled = process_overlay_key (display, screen, event, window);
       if (handled)
         return TRUE;
 
@@ -2150,8 +2149,7 @@ meta_display_process_key_event (MetaDisplay     *display,
   /* Do the normal keybindings */
   return process_event (display->key_bindings,
                         display->n_key_bindings,
-                        display, screen, window, event,
-                        !all_keys_grabbed && window);
+                        display, screen, window, event);
 }
 
 static gboolean