diff --git a/gtk/gtkmain.c b/gtk/gtkmain.c
index 362800ee6d..9eac06ffde 100644
--- a/gtk/gtkmain.c
+++ b/gtk/gtkmain.c
@@ -1998,15 +1998,6 @@ gtk_main_do_event (GdkEvent *event)
 
     case GDK_KEY_PRESS:
     case GDK_KEY_RELEASE:
-      /* make focus visible in a window that receives a key event */
-      {
-        GtkRoot *root;
-
-        root = gtk_widget_get_root (grab_widget);
-        if (GTK_IS_WINDOW (root))
-          gtk_window_set_focus_visible (GTK_WINDOW (root), TRUE);
-      }
-
       /* Catch alt press to enable auto-mnemonics;
        * menus are handled elsewhere
        * FIXME: this does not work with mnemonic modifiers other than Alt
diff --git a/gtk/gtkwindow.c b/gtk/gtkwindow.c
index 25b6fc63a5..3b4b8b7bbe 100644
--- a/gtk/gtkwindow.c
+++ b/gtk/gtkwindow.c
@@ -406,6 +406,7 @@ static void gtk_window_size_allocate      (GtkWidget         *widget,
 static gboolean gtk_window_close_request  (GtkWindow         *window);
 static void gtk_window_focus_in           (GtkWidget         *widget);
 static void gtk_window_focus_out          (GtkWidget         *widget);
+static gboolean gtk_window_key_press      (GtkWidget         *widget);
 
 static void     surface_state_changed     (GtkWidget          *widget);
 static void     surface_size_changed      (GtkWidget          *widget,
@@ -1864,10 +1865,14 @@ gtk_window_init (GtkWindow *window)
   gtk_widget_add_controller (widget, motion_controller);
 
   priv->key_controller = gtk_event_controller_key_new ();
+  gtk_event_controller_set_name (controller, "window focus");
+  gtk_event_controller_set_propagation_phase (controller, GTK_PHASE_CAPTURE);
   g_signal_connect_swapped (priv->key_controller, "focus-in",
                             G_CALLBACK (gtk_window_focus_in), window);
   g_signal_connect_swapped (priv->key_controller, "focus-out",
                             G_CALLBACK (gtk_window_focus_out), window);
+  g_signal_connect_swapped (priv->key_controller, "key-pressed",
+                            G_CALLBACK (gtk_window_key_press), window);
   gtk_widget_add_controller (widget, priv->key_controller);
 }
 
@@ -6207,6 +6212,16 @@ gtk_window_focus_out (GtkWidget *widget)
   gtk_window_set_mnemonics_visible (window, FALSE);
 }
 
+static gboolean
+gtk_window_key_press (GtkWidget *widget)
+{
+  GtkWindow *window = GTK_WINDOW (widget);
+
+  gtk_window_set_focus_visible (window, TRUE);
+
+  return FALSE;
+}
+
 static GtkWindowPopover *
 _gtk_window_has_popover (GtkWindow *window,
                          GtkWidget *widget)