diff --git a/testsuite/gtk/expander.c b/testsuite/gtk/expander.c
index e651d8a10c..fc49bc0e76 100644
--- a/testsuite/gtk/expander.c
+++ b/testsuite/gtk/expander.c
@@ -23,6 +23,10 @@
  */
 #include <gtk/gtk.h>
 
+#ifdef GDK_WINDOWING_X11
+#include <gdk/gdkx.h>
+#endif
+
 static void
 test_click_expander (void)
 {
@@ -65,6 +69,7 @@ test_click_content_widget (void)
   GtkWidget *entry = gtk_entry_new ();
   gboolean expanded;
   gboolean simsuccess;
+
   gtk_container_add (GTK_CONTAINER (expander), entry);
   gtk_container_add (GTK_CONTAINER (gtk_bin_get_child (GTK_BIN (window))), expander);
   gtk_expander_set_expanded (GTK_EXPANDER (expander), TRUE);
@@ -89,7 +94,16 @@ main (int   argc,
       char *argv[])
 {
   gtk_test_init (&argc, &argv);
+
+#ifdef GDK_WINDOWING_X11
+  if (GDK_IS_X11_DISPLAY (gdk_display_get_default ())) ;
+    return 0; /* gtk_test functions don't work well elsewhere */
+#else
+  return 0;
+#endif
+
   g_test_add_func ("/expander/click-expander", test_click_expander);
   g_test_add_func ("/expander/click-content-widget", test_click_content_widget);
+
   return g_test_run();
 }
diff --git a/testsuite/gtk/notify.c b/testsuite/gtk/notify.c
index 1ae3ab6fc2..91492cc1eb 100644
--- a/testsuite/gtk/notify.c
+++ b/testsuite/gtk/notify.c
@@ -19,6 +19,12 @@
 #include <string.h>
 #include <gtk/gtk.h>
 #include <gtk/gtkunixprint.h>
+#ifdef GDK_WINDOWING_X11
+#include <gtk/gtkx.h>
+#endif
+#ifdef GDK_WINDOWING_WAYLAND
+#include "gdk/wayland/gdkwayland.h"
+#endif
 
 typedef struct
 {
@@ -407,7 +413,24 @@ test_type (gconstpointer data)
   /* These rely on a d-bus session bus */
   if (g_type_is_a (type, GTK_TYPE_MOUNT_OPERATION))
     return;
- 
+
+  /* Backend-specific */
+#ifdef GDK_WINDOWING_X11
+  if (GDK_IS_X11_DISPLAY (gdk_display_get_default ())) ;
+  else
+#endif
+  if (g_type_is_a (type, GTK_TYPE_PLUG) ||
+      g_type_is_a (type, GTK_TYPE_SOCKET))
+    return;
+
+#ifdef GDK_WINDOWING_WAYLAND
+  if (GDK_IS_WAYLAND_DISPLAY (gdk_display_get_default ()))
+    {
+      if (g_type_is_a (type, GTK_TYPE_STATUS_ICON))
+        return;
+    }
+#endif
+
   klass = g_type_class_ref (type);
 
   if (g_type_is_a (type, GTK_TYPE_SETTINGS))
diff --git a/testsuite/gtk/window.c b/testsuite/gtk/window.c
index fa8dfc6b31..c28b8a07ed 100644
--- a/testsuite/gtk/window.c
+++ b/testsuite/gtk/window.c
@@ -375,34 +375,35 @@ test_hide_titlebar_when_maximized (void)
   gtk_main ();
 
 #ifdef GDK_WINDOWING_X11
-  {
-    Atom type;
-    gint format;
-    gulong nitems;
-    gulong bytes_after;
-    gulong *hide = NULL;
+  if (GDK_IS_X11_SCREEN (gtk_widget_get_screen (window)))
+    {
+      Atom type;
+      gint format;
+      gulong nitems;
+      gulong bytes_after;
+      gulong *hide = NULL;
 
-    XGetWindowProperty (gdk_x11_get_default_xdisplay (),
-                        GDK_WINDOW_XID (gtk_widget_get_window (window)),
-                        gdk_x11_get_xatom_by_name ("_GTK_HIDE_TITLEBAR_WHEN_MAXIMIZED"),
-                        0,
-                        G_MAXLONG,
-                        False,
-                        XA_CARDINAL,
-                        &type,
-                        &format,
-                        &nitems,
-                        &bytes_after,
-                        (guchar **) &hide);
+      XGetWindowProperty (gdk_x11_get_default_xdisplay (),
+                          GDK_WINDOW_XID (gtk_widget_get_window (window)),
+                          gdk_x11_get_xatom_by_name ("_GTK_HIDE_TITLEBAR_WHEN_MAXIMIZED"),
+                          0,
+                          G_MAXLONG,
+                          False,
+                          XA_CARDINAL,
+                          &type,
+                          &format,
+                          &nitems,
+                          &bytes_after,
+                          (guchar **) &hide);
 
-    g_assert_cmpint (type, !=, None);
-    g_assert_cmpint (type, ==, XA_CARDINAL);
-    g_assert_cmpint (format, ==, 32);
-    g_assert_cmpint (nitems, ==, 1);
-    g_assert_cmpint (hide[0], ==, 1);
+      g_assert_cmpint (type, !=, None);
+      g_assert_cmpint (type, ==, XA_CARDINAL);
+      g_assert_cmpint (format, ==, 32);
+      g_assert_cmpint (nitems, ==, 1);
+      g_assert_cmpint (hide[0], ==, 1);
 
-    XFree (hide);
-  }
+      XFree (hide);
+    }
 #endif
 
   gtk_widget_destroy (window);