diff --git a/block/stream.c b/block/stream.c
index 6e281c71ac..6a525a5edf 100644
--- a/block/stream.c
+++ b/block/stream.c
@@ -65,6 +65,7 @@ static int stream_prepare(Job *job)
     BlockDriverState *bs = blk_bs(bjob->blk);
     BlockDriverState *unfiltered_bs = bdrv_skip_filters(bs);
     BlockDriverState *base = bdrv_filter_or_cow_bs(s->above_base);
+    BlockDriverState *unfiltered_base = bdrv_skip_filters(base);
     Error *local_err = NULL;
     int ret = 0;
 
@@ -73,10 +74,10 @@ static int stream_prepare(Job *job)
 
     if (bdrv_cow_child(unfiltered_bs)) {
         const char *base_id = NULL, *base_fmt = NULL;
-        if (base) {
-            base_id = s->backing_file_str;
-            if (base->drv) {
-                base_fmt = base->drv->format_name;
+        if (unfiltered_base) {
+            base_id = s->backing_file_str ?: unfiltered_base->filename;
+            if (unfiltered_base->drv) {
+                base_fmt = unfiltered_base->drv->format_name;
             }
         }
         bdrv_set_backing_hd(unfiltered_bs, base, &local_err);
diff --git a/blockdev.c b/blockdev.c
index e496356e10..8c03de582c 100644
--- a/blockdev.c
+++ b/blockdev.c
@@ -2511,7 +2511,6 @@ void qmp_block_stream(bool has_job_id, const char *job_id, const char *device,
     BlockDriverState *base_bs = NULL;
     AioContext *aio_context;
     Error *local_err = NULL;
-    const char *base_name = NULL;
     int job_flags = JOB_DEFAULT;
 
     if (!has_on_error) {
@@ -2539,7 +2538,6 @@ void qmp_block_stream(bool has_job_id, const char *job_id, const char *device,
             goto out;
         }
         assert(bdrv_get_aio_context(base_bs) == aio_context);
-        base_name = base;
     }
 
     if (has_base_node) {
@@ -2554,7 +2552,6 @@ void qmp_block_stream(bool has_job_id, const char *job_id, const char *device,
         }
         assert(bdrv_get_aio_context(base_bs) == aio_context);
         bdrv_refresh_filename(base_bs);
-        base_name = base_bs->filename;
     }
 
     /* Check for op blockers in the whole chain between bs and base */
@@ -2574,9 +2571,6 @@ void qmp_block_stream(bool has_job_id, const char *job_id, const char *device,
         goto out;
     }
 
-    /* backing_file string overrides base bs filename */
-    base_name = has_backing_file ? backing_file : base_name;
-
     if (has_auto_finalize && !auto_finalize) {
         job_flags |= JOB_MANUAL_FINALIZE;
     }
@@ -2584,7 +2578,7 @@ void qmp_block_stream(bool has_job_id, const char *job_id, const char *device,
         job_flags |= JOB_MANUAL_DISMISS;
     }
 
-    stream_start(has_job_id ? job_id : NULL, bs, base_bs, base_name,
+    stream_start(has_job_id ? job_id : NULL, bs, base_bs, backing_file,
                  job_flags, has_speed ? speed : 0, on_error,
                  filter_node_name, &local_err);
     if (local_err) {