diff --git a/xkb/xkb.c b/xkb/xkb.c
index 2e9dcbf5de..1a443c80ff 100644
--- a/xkb/xkb.c
+++ b/xkb/xkb.c
@@ -3794,7 +3794,8 @@ XkbAssembleNames(ClientPtr client, XkbDescPtr xkb, xkbGetNamesReply rep, x_rpcbu
             XkbKeyTypePtr type = xkb->map->types;
 
             for (i = 0; i < rep.nTypes; i++, type++) {
-                x_rpcbuf_write_CARD8(rpcbuf, type->num_levels);
+                /* Either no name or all of them, even empty ones */
+                x_rpcbuf_write_CARD8(rpcbuf, type->level_names ? type->num_levels : 0);
             }
             x_rpcbuf_pad(rpcbuf);
 
diff --git a/xkb/xkbUtils.c b/xkb/xkbUtils.c
index 68ee0b0888..ad71cd9cec 100644
--- a/xkb/xkbUtils.c
+++ b/xkb/xkbUtils.c
@@ -1046,7 +1046,7 @@ _XkbCopyClientMap(XkbDescPtr src, XkbDescPtr dst)
                     if (dtype->num_levels && dtype->level_names &&
                         i < dst->map->num_types)
                         free(dtype->level_names);
-                    dtype->num_levels = 0;
+                    dtype->num_levels = stype->num_levels;
                     dtype->level_names = NULL;
                 }