diff --git a/apparmor.d/abstractions/mesa.d/complete b/apparmor.d/abstractions/mesa.d/complete
index d8b2f4a3..7c0394ca 100644
--- a/apparmor.d/abstractions/mesa.d/complete
+++ b/apparmor.d/abstractions/mesa.d/complete
@@ -3,12 +3,12 @@
 # SPDX-License-Identifier: GPL-2.0-only
 
   # Extra Mesa rules for GDM
-  /var/lib/gdm/.cache/ w,
-  /var/lib/gdm/.cache/mesa_shader_cache/ rw,
-  /var/lib/gdm/.cache/mesa_shader_cache/index rw,
-  /var/lib/gdm/.cache/mesa_shader_cache/@{h}@{h}/ rw,
-  /var/lib/gdm/.cache/mesa_shader_cache/@{h}@{h}/@{hex} rw,
-  /var/lib/gdm/.cache/mesa_shader_cache/@{h}@{h}/@{hex}.tmp rwk,
+  /var/lib/gdm{3,}/.cache/ w,
+  /var/lib/gdm{3,}/.cache/mesa_shader_cache/ rw,
+  /var/lib/gdm{3,}/.cache/mesa_shader_cache/index rw,
+  /var/lib/gdm{3,}/.cache/mesa_shader_cache/@{h}@{h}/ rw,
+  /var/lib/gdm{3,}/.cache/mesa_shader_cache/@{h}@{h}/@{hex} rw,
+  /var/lib/gdm{3,}/.cache/mesa_shader_cache/@{h}@{h}/@{hex}.tmp rwk,
 
   # Extra Mesa rules for SDDM
   /var/lib/sddm/.cache/ w,