diff --git a/block/backup.c b/block/backup.c
index 4869f1e5da..687d2882bc 100644
--- a/block/backup.c
+++ b/block/backup.c
@@ -233,18 +233,16 @@ static void backup_init_bcs_bitmap(BackupBlockJob *job)
     BdrvDirtyBitmap *bcs_bitmap = block_copy_dirty_bitmap(job->bcs);
 
     if (job->sync_mode == MIRROR_SYNC_MODE_BITMAP) {
+        bdrv_clear_dirty_bitmap(bcs_bitmap, NULL);
         ret = bdrv_dirty_bitmap_merge_internal(bcs_bitmap, job->sync_bitmap,
                                                NULL, true);
         assert(ret);
-    } else {
-        if (job->sync_mode == MIRROR_SYNC_MODE_TOP) {
-            /*
-             * We can't hog the coroutine to initialize this thoroughly.
-             * Set a flag and resume work when we are able to yield safely.
-             */
-            block_copy_set_skip_unallocated(job->bcs, true);
-        }
-        bdrv_set_dirty_bitmap(bcs_bitmap, 0, job->len);
+    } else if (job->sync_mode == MIRROR_SYNC_MODE_TOP) {
+        /*
+         * We can't hog the coroutine to initialize this thoroughly.
+         * Set a flag and resume work when we are able to yield safely.
+         */
+        block_copy_set_skip_unallocated(job->bcs, true);
     }
 
     estimate = bdrv_get_dirty_count(bcs_bitmap);
diff --git a/block/copy-before-write.c b/block/copy-before-write.c
index 1cefcade78..2efe098aae 100644
--- a/block/copy-before-write.c
+++ b/block/copy-before-write.c
@@ -147,6 +147,7 @@ static void cbw_child_perm(BlockDriverState *bs, BdrvChild *c,
 static int cbw_init(BlockDriverState *bs, QDict *options, Error **errp)
 {
     BDRVCopyBeforeWriteState *s = bs->opaque;
+    BdrvDirtyBitmap *copy_bitmap;
 
     bs->file = bdrv_open_child(NULL, options, "file", bs, &child_of_bds,
                                BDRV_CHILD_FILTERED | BDRV_CHILD_PRIMARY,
@@ -174,6 +175,9 @@ static int cbw_init(BlockDriverState *bs, QDict *options, Error **errp)
         return -EINVAL;
     }
 
+    copy_bitmap = block_copy_dirty_bitmap(s->bcs);
+    bdrv_set_dirty_bitmap(copy_bitmap, 0, bdrv_dirty_bitmap_size(copy_bitmap));
+
     return 0;
 }