diff --git a/config/apparmor/abstractions/container-base b/config/apparmor/abstractions/container-base
index 9452f6608..0aacb6aa1 100644
--- a/config/apparmor/abstractions/container-base
+++ b/config/apparmor/abstractions/container-base
@@ -93,18 +93,15 @@
   # deny reads from debugfs
   deny /sys/kernel/debug/{,**} rwklx,
 
-  # allow paths to be made shared, rshared, private or rprivate
-  mount options=(rw,shared) -> /,
-  mount options=(rw,shared) -> /**,
-
-  mount options=(rw,rshared) -> /,
-  mount options=(rw,rshared) -> /**,
-
-  mount options=(rw,private) -> /,
-  mount options=(rw,private) -> /**,
-
-  mount options=(rw,rprivate) -> /,
-  mount options=(rw,rprivate) -> /**,
+  # allow paths to be made slave, shared, private or unbindable
+  mount options=(rw,make-slave) -> **,
+  mount options=(rw,make-rslave) -> **,
+  mount options=(rw,make-shared) -> **,
+  mount options=(rw,make-rshared) -> **,
+  mount options=(rw,make-private) -> **,
+  mount options=(rw,make-rprivate) -> **,
+  mount options=(rw,make-unbindable) -> **,
+  mount options=(rw,make-runbindable) -> **,
 
   # allow bind-mounts of anything except /proc, /sys and /dev
   mount options=(rw,bind) /[^spd]*{,/**},
@@ -124,6 +121,24 @@
   mount options=(rw,bind) /sy[^s]*{,/**},
   mount options=(rw,bind) /sys?*{,/**},
 
+  # allow moving mounts except for /proc, /sys and /dev
+  mount options=(rw,move) /[^spd]*{,/**},
+  mount options=(rw,move) /d[^e]*{,/**},
+  mount options=(rw,move) /de[^v]*{,/**},
+  mount options=(rw,move) /dev/.[^l]*{,/**},
+  mount options=(rw,move) /dev/.l[^x]*{,/**},
+  mount options=(rw,move) /dev/.lx[^c]*{,/**},
+  mount options=(rw,move) /dev/.lxc?*{,/**},
+  mount options=(rw,move) /dev/[^.]*{,/**},
+  mount options=(rw,move) /dev?*{,/**},
+  mount options=(rw,move) /p[^r]*{,/**},
+  mount options=(rw,move) /pr[^o]*{,/**},
+  mount options=(rw,move) /pro[^c]*{,/**},
+  mount options=(rw,move) /proc?*{,/**},
+  mount options=(rw,move) /s[^y]*{,/**},
+  mount options=(rw,move) /sy[^s]*{,/**},
+  mount options=(rw,move) /sys?*{,/**},
+
   # generated by: lxc-generate-aa-rules.py container-rules.base
   deny /proc/sys/[^kn]*{,/**} wklx,
   deny /proc/sys/k[^e]*{,/**} wklx,
diff --git a/config/apparmor/abstractions/container-base.in b/config/apparmor/abstractions/container-base.in
index 68db43db4..5bc9b28bf 100644
--- a/config/apparmor/abstractions/container-base.in
+++ b/config/apparmor/abstractions/container-base.in
@@ -93,18 +93,16 @@
   # deny reads from debugfs
   deny /sys/kernel/debug/{,**} rwklx,
 
-  # allow paths to be made shared, rshared, private or rprivate
-  mount options=(rw,shared) -> /,
-  mount options=(rw,shared) -> /**,
-
-  mount options=(rw,rshared) -> /,
-  mount options=(rw,rshared) -> /**,
-
-  mount options=(rw,private) -> /,
-  mount options=(rw,private) -> /**,
-
-  mount options=(rw,rprivate) -> /,
-  mount options=(rw,rprivate) -> /**,
+  # allow paths to be made slave, shared, private or unbindable
+  # FIXME: This currently doesn't work due to the apparmor parser treating those as allowing all mounts.
+#  mount options=(rw,make-slave) -> **,
+#  mount options=(rw,make-rslave) -> **,
+#  mount options=(rw,make-shared) -> **,
+#  mount options=(rw,make-rshared) -> **,
+#  mount options=(rw,make-private) -> **,
+#  mount options=(rw,make-rprivate) -> **,
+#  mount options=(rw,make-unbindable) -> **,
+#  mount options=(rw,make-runbindable) -> **,
 
   # allow bind-mounts of anything except /proc, /sys and /dev
   mount options=(rw,bind) /[^spd]*{,/**},
@@ -124,3 +122,21 @@
   mount options=(rw,bind) /sy[^s]*{,/**},
   mount options=(rw,bind) /sys?*{,/**},
 
+  # allow moving mounts except for /proc, /sys and /dev
+  mount options=(rw,move) /[^spd]*{,/**},
+  mount options=(rw,move) /d[^e]*{,/**},
+  mount options=(rw,move) /de[^v]*{,/**},
+  mount options=(rw,move) /dev/.[^l]*{,/**},
+  mount options=(rw,move) /dev/.l[^x]*{,/**},
+  mount options=(rw,move) /dev/.lx[^c]*{,/**},
+  mount options=(rw,move) /dev/.lxc?*{,/**},
+  mount options=(rw,move) /dev/[^.]*{,/**},
+  mount options=(rw,move) /dev?*{,/**},
+  mount options=(rw,move) /p[^r]*{,/**},
+  mount options=(rw,move) /pr[^o]*{,/**},
+  mount options=(rw,move) /pro[^c]*{,/**},
+  mount options=(rw,move) /proc?*{,/**},
+  mount options=(rw,move) /s[^y]*{,/**},
+  mount options=(rw,move) /sy[^s]*{,/**},
+  mount options=(rw,move) /sys?*{,/**},
+