diff --git a/glamor/glamor_core.c b/glamor/glamor_core.c
index 6b10e97ab..a6a603973 100644
--- a/glamor/glamor_core.c
+++ b/glamor/glamor_core.c
@@ -106,6 +106,19 @@ Bool
 glamor_prepare_access(DrawablePtr drawable, glamor_access_t access)
 {
     PixmapPtr pixmap = glamor_get_drawable_pixmap(drawable);
+    glamor_pixmap_private *pixmap_priv = glamor_get_pixmap_private(pixmap);
+
+    if (pixmap->devPrivate.ptr) {
+        /* Already mapped, nothing needs to be done.  Note that we
+         * aren't allowing promotion from RO to RW, because it would
+         * require re-mapping the PBO.
+         */
+        assert(!GLAMOR_PIXMAP_PRIV_HAS_FBO(pixmap_priv) ||
+               access == GLAMOR_ACCESS_RO ||
+               pixmap_priv->base.mapped_for_write);
+        return TRUE;
+    }
+    pixmap_priv->base.map_access = access;
 
     return glamor_download_pixmap_to_cpu(pixmap, access);
 }
@@ -301,7 +314,15 @@ glamor_finish_access(DrawablePtr drawable, glamor_access_t access_mode)
     if (!GLAMOR_PIXMAP_PRIV_HAS_FBO_DOWNLOADED(pixmap_priv))
         return;
 
-    if (access_mode != GLAMOR_ACCESS_RO) {
+    /* If we are doing a series of unmaps from a nested map, we're
+     * done.  None of the callers do any rendering to maps after
+     * starting an unmap sequence, so we don't need to delay until the
+     * last nested unmap.
+     */
+    if (!pixmap->devPrivate.ptr)
+        return;
+
+    if (pixmap_priv->base.map_access == GLAMOR_ACCESS_RW) {
         glamor_restore_pixmap_to_texture(pixmap);
     }
 
diff --git a/glamor/glamor_priv.h b/glamor/glamor_priv.h
index 3cc0d2407..776de06ef 100644
--- a/glamor/glamor_priv.h
+++ b/glamor/glamor_priv.h
@@ -410,6 +410,12 @@ typedef struct glamor_pixmap_clipped_regions {
 typedef struct glamor_pixmap_private_base {
     glamor_pixmap_type_t type;
     enum glamor_fbo_state gl_fbo;
+    /**
+     * If devPrivate.ptr is non-NULL (meaning we're within
+     * glamor_prepare_access), determies whether we should re-upload
+     * that data on glamor_finish_access().
+     */
+    glamor_access_t map_access;
     unsigned char is_picture:1;
     unsigned char gl_tex:1;
     glamor_pixmap_fbo *fbo;