diff --git a/block/qcow2.c b/block/qcow2.c
index b74cbeb047..2bb536b014 100644
--- a/block/qcow2.c
+++ b/block/qcow2.c
@@ -2823,8 +2823,15 @@ int qcow2_update_header(BlockDriverState *bs)
         buflen -= ret;
     }
 
-    /* Feature table */
-    if (s->qcow_version >= 3) {
+    /*
+     * Feature table.  A mere 8 feature names occupies 392 bytes, and
+     * when coupled with the v3 minimum header of 104 bytes plus the
+     * 8-byte end-of-extension marker, that would leave only 8 bytes
+     * for a backing file name in an image with 512-byte clusters.
+     * Thus, we choose to omit this header for cluster sizes 4k and
+     * smaller.
+     */
+    if (s->qcow_version >= 3 && s->cluster_size > 4096) {
         static const Qcow2Feature features[] = {
             {
                 .type = QCOW2_FEAT_TYPE_INCOMPATIBLE,
diff --git a/tests/qemu-iotests/036 b/tests/qemu-iotests/036
index 512598421c..cf522de7a1 100755
--- a/tests/qemu-iotests/036
+++ b/tests/qemu-iotests/036
@@ -44,8 +44,10 @@ trap "_cleanup; exit \$status" 0 1 2 3 15
 _supported_fmt qcow2
 _supported_proto file
 # Only qcow2v3 and later supports feature bits;
-# qcow2.py does not support external data files
-_unsupported_imgopts 'compat=0.10' data_file
+# qcow2.py does not support external data files;
+# this test requires a cluster size large enough for the feature table
+_unsupported_imgopts 'compat=0.10' data_file \
+		     'cluster_size=\(512\|1024\|2048\|4096\)'
 
 echo
 echo === Image with unknown incompatible feature bit ===
diff --git a/tests/qemu-iotests/061 b/tests/qemu-iotests/061
index 36b040491f..ce285d3084 100755
--- a/tests/qemu-iotests/061
+++ b/tests/qemu-iotests/061
@@ -44,8 +44,10 @@ _supported_os Linux
 # Conversion between different compat versions can only really work
 # with refcount_bits=16;
 # we have explicit tests for data_file here, but the whole test does
-# not work with it
-_unsupported_imgopts 'refcount_bits=\([^1]\|.\([^6]\|$\)\)' data_file
+# not work with it;
+# we have explicit tests for various cluster sizes, the remaining tests
+# require the default 64k cluster
+_unsupported_imgopts 'refcount_bits=\([^1]\|.\([^6]\|$\)\)' data_file cluster_size
 
 echo
 echo "=== Testing version downgrade with zero expansion ==="