diff --git a/block/qcow.c b/block/qcow.c
index ccbe9e0d2c14fc531695d914e5f562fb87da987e..055896910eab9c6946ff66f4265f594e5218f47c 100644
--- a/block/qcow.c
+++ b/block/qcow.c
@@ -215,7 +215,7 @@ static int qcow_open(BlockDriverState *bs, QDict *options, int flags,
     /* read the backing file name */
     if (header.backing_file_offset != 0) {
         len = header.backing_file_size;
-        if (len > 1023 || len > sizeof(bs->backing_file)) {
+        if (len > 1023 || len >= sizeof(bs->backing_file)) {
             error_setg(errp, "Backing file name too long");
             ret = -EINVAL;
             goto fail;
diff --git a/block/qcow2.c b/block/qcow2.c
index dbaf016bc706c9c3e67384331136e0ad94497a8a..7e614d76a430ba0fffaaccc7e311562d2312c09b 100644
--- a/block/qcow2.c
+++ b/block/qcow2.c
@@ -869,7 +869,7 @@ static int qcow2_open(BlockDriverState *bs, QDict *options, int flags,
     if (header.backing_file_offset != 0) {
         len = header.backing_file_size;
         if (len > MIN(1023, s->cluster_size - header.backing_file_offset) ||
-            len > sizeof(bs->backing_file)) {
+            len >= sizeof(bs->backing_file)) {
             error_setg(errp, "Backing file name too long");
             ret = -EINVAL;
             goto fail;