diff --git a/block/qcow.c b/block/qcow.c
index e60df23..e8038e5 100644
--- a/block/qcow.c
+++ b/block/qcow.c
@@ -139,6 +139,14 @@
         goto fail;
     }
 
+    /* l2_bits specifies number of entries; storing a uint64_t in each entry,
+     * so bytes = num_entries << 3. */
+    if (header.l2_bits < 9 - 3 || header.l2_bits > 16 - 3) {
+        error_setg(errp, "L2 table size must be between 512 and 64k");
+        ret = -EINVAL;
+        goto fail;
+    }
+
     if (header.crypt_method > QCOW_CRYPT_AES) {
         error_setg(errp, "invalid encryption method in qcow header");
         ret = -EINVAL;
diff --git a/tests/qemu-iotests/092 b/tests/qemu-iotests/092
index d060e6f..fb8bacc 100755
--- a/tests/qemu-iotests/092
+++ b/tests/qemu-iotests/092
@@ -44,6 +44,7 @@
 _supported_os Linux
 
 offset_cluster_bits=32
+offset_l2_bits=33
 
 echo
 echo "== Invalid cluster size =="
@@ -57,6 +58,20 @@
 poke_file "$TEST_IMG" "$offset_cluster_bits" "\x11"
 { $QEMU_IO -c "read 0 512" $TEST_IMG; } 2>&1 | _filter_qemu_io | _filter_testdir
 
+echo
+echo "== Invalid L2 table size =="
+_make_test_img 64M
+poke_file "$TEST_IMG" "$offset_l2_bits" "\xff"
+{ $QEMU_IO -c "read 0 512" $TEST_IMG; } 2>&1 | _filter_qemu_io | _filter_testdir
+poke_file "$TEST_IMG" "$offset_l2_bits" "\x05"
+{ $QEMU_IO -c "read 0 512" $TEST_IMG; } 2>&1 | _filter_qemu_io | _filter_testdir
+poke_file "$TEST_IMG" "$offset_l2_bits" "\x0e"
+{ $QEMU_IO -c "read 0 512" $TEST_IMG; } 2>&1 | _filter_qemu_io | _filter_testdir
+
+# 1 << 0x1b = 2^31 / L2_CACHE_SIZE
+poke_file "$TEST_IMG" "$offset_l2_bits" "\x1b"
+{ $QEMU_IO -c "read 0 512" $TEST_IMG; } 2>&1 | _filter_qemu_io | _filter_testdir
+
 # success, all done
 echo "*** done"
 rm -f $seq.full
diff --git a/tests/qemu-iotests/092.out b/tests/qemu-iotests/092.out
index 8bf8158..73918b3 100644
--- a/tests/qemu-iotests/092.out
+++ b/tests/qemu-iotests/092.out
@@ -10,4 +10,15 @@
 no file open, try 'help open'
 qemu-io: can't open device TEST_DIR/t.qcow: Cluster size must be between 512 and 64k
 no file open, try 'help open'
+
+== Invalid L2 table size ==
+Formatting 'TEST_DIR/t.IMGFMT', fmt=IMGFMT size=67108864 
+qemu-io: can't open device TEST_DIR/t.qcow: L2 table size must be between 512 and 64k
+no file open, try 'help open'
+qemu-io: can't open device TEST_DIR/t.qcow: L2 table size must be between 512 and 64k
+no file open, try 'help open'
+qemu-io: can't open device TEST_DIR/t.qcow: L2 table size must be between 512 and 64k
+no file open, try 'help open'
+qemu-io: can't open device TEST_DIR/t.qcow: L2 table size must be between 512 and 64k
+no file open, try 'help open'
 *** done