diff --git a/block/qcow2-cluster.c b/block/qcow2-cluster.c
index e444e53e136a5cb98ff99386686a397cd8632f6e..f88118cdc5626933dd48740b227665513b69dc8b 100644
--- a/block/qcow2-cluster.c
+++ b/block/qcow2-cluster.c
@@ -39,6 +39,9 @@ int qcow2_grow_l1_table(BlockDriverState *bs, int min_size)
     new_l1_size = s->l1_size;
     if (min_size <= new_l1_size)
         return 0;
+    if (new_l1_size == 0) {
+        new_l1_size = 1;
+    }
     while (min_size > new_l1_size) {
         new_l1_size = (new_l1_size * 3 + 1) / 2;
     }
diff --git a/block/qcow2.c b/block/qcow2.c
index a9e768268a6df9aeaaa4a6448dcd4f8c03dba4b1..3954cf13984c3a0c9df0143132fd8369f33c7e36 100644
--- a/block/qcow2.c
+++ b/block/qcow2.c
@@ -166,8 +166,7 @@ static int qcow_open(BlockDriverState *bs, const char *filename, int flags)
 
     if (header.magic != QCOW_MAGIC || header.version != QCOW_VERSION)
         goto fail;
-    if (header.size <= 1 ||
-        header.cluster_bits < MIN_CLUSTER_BITS ||
+    if (header.cluster_bits < MIN_CLUSTER_BITS ||
         header.cluster_bits > MAX_CLUSTER_BITS)
         goto fail;
     if (header.crypt_method > QCOW_CRYPT_AES)
@@ -200,13 +199,15 @@ static int qcow_open(BlockDriverState *bs, const char *filename, int flags)
     if (s->l1_size < s->l1_vm_state_index)
         goto fail;
     s->l1_table_offset = header.l1_table_offset;
-    s->l1_table = qemu_mallocz(
-        align_offset(s->l1_size * sizeof(uint64_t), 512));
-    if (bdrv_pread(s->hd, s->l1_table_offset, s->l1_table, s->l1_size * sizeof(uint64_t)) !=
-        s->l1_size * sizeof(uint64_t))
-        goto fail;
-    for(i = 0;i < s->l1_size; i++) {
-        be64_to_cpus(&s->l1_table[i]);
+    if (s->l1_size > 0) {
+        s->l1_table = qemu_mallocz(
+            align_offset(s->l1_size * sizeof(uint64_t), 512));
+        if (bdrv_pread(s->hd, s->l1_table_offset, s->l1_table, s->l1_size * sizeof(uint64_t)) !=
+            s->l1_size * sizeof(uint64_t))
+            goto fail;
+        for(i = 0;i < s->l1_size; i++) {
+            be64_to_cpus(&s->l1_table[i]);
+        }
     }
     /* alloc L2 cache */
     s->l2_cache = qemu_malloc(s->l2_size * L2_CACHE_SIZE * sizeof(uint64_t));