diff --git a/block/qcow2-cluster.c b/block/qcow2-cluster.c
index fb91fd8979e726f0a77278358be0f49cc2df25e4..31077d8102180059ab540a38fcf106dece26aa5f 100644
--- a/block/qcow2-cluster.c
+++ b/block/qcow2-cluster.c
@@ -1511,7 +1511,8 @@ static int discard_single_l2(BlockDriverState *bs, uint64_t offset,
                 break;
 
             case QCOW2_CLUSTER_ZERO:
-                if (!full_discard) {
+                /* Preallocated zero clusters should be discarded in any case */
+                if (!full_discard && (old_l2_entry & L2E_OFFSET_MASK) == 0) {
                     continue;
                 }
                 break;