diff --git a/tests/qemu-iotests/036 b/tests/qemu-iotests/036
index 5f929ad3be..bbaf0ef45b 100755
--- a/tests/qemu-iotests/036
+++ b/tests/qemu-iotests/036
@@ -43,9 +43,8 @@ trap "_cleanup; exit \$status" 0 1 2 3 15
 # This tests qcow2-specific low-level functionality
 _supported_fmt qcow2
 _supported_proto file
-
 # Only qcow2v3 and later supports feature bits
-IMGOPTS="compat=1.1"
+_unsupported_imgopts 'compat=0.10'
 
 echo
 echo === Image with unknown incompatible feature bit ===
diff --git a/tests/qemu-iotests/060 b/tests/qemu-iotests/060
index 7439be894b..932bc2f3f9 100755
--- a/tests/qemu-iotests/060
+++ b/tests/qemu-iotests/060
@@ -48,6 +48,8 @@ _filter_io_error()
 _supported_fmt qcow2
 _supported_proto file
 _supported_os Linux
+# These tests only work for compat=1.1 images with refcount_bits=16
+_unsupported_imgopts 'compat=0.10' 'refcount_bits=\([^1]\|.\([^6]\|$\)\)'
 
 # The repair process will create a large file - so check for availability first
 _require_large_file 64G
@@ -58,8 +60,6 @@ l1_offset=196608 # 0x30000 (XXX: just an assumption)
 l2_offset=262144 # 0x40000 (XXX: just an assumption)
 l2_offset_after_snapshot=524288 # 0x80000 (XXX: just an assumption)
 
-IMGOPTS="compat=1.1"
-
 OPEN_RW="open -o overlap-check=all $TEST_IMG"
 # Overlap checks are done before write operations only, therefore opening an
 # image read-only makes the overlap-check option irrelevant
diff --git a/tests/qemu-iotests/062 b/tests/qemu-iotests/062
index 79738b1c26..0df8667e5a 100755
--- a/tests/qemu-iotests/062
+++ b/tests/qemu-iotests/062
@@ -40,8 +40,9 @@ trap "_cleanup; exit \$status" 0 1 2 3 15
 # This tests qcow2-specific low-level functionality
 _supported_fmt qcow2
 _supported_proto generic
+# We need zero clusters and snapshots
+_unsupported_imgopts 'compat=0.10' 'refcount_bits=1[^0-9]'
 
-IMGOPTS="compat=1.1"
 IMG_SIZE=64M
 
 echo
diff --git a/tests/qemu-iotests/066 b/tests/qemu-iotests/066
index cacbdb6ae0..71e8df598a 100755
--- a/tests/qemu-iotests/066
+++ b/tests/qemu-iotests/066
@@ -39,9 +39,10 @@ trap "_cleanup; exit \$status" 0 1 2 3 15
 # This tests qcow2-specific low-level functionality
 _supported_fmt qcow2
 _supported_proto generic
+# We need zero clusters and snapshots
+_unsupported_imgopts 'compat=0.10' 'refcount_bits=1[^0-9]'
 
 # Intentionally create an unaligned image
-IMGOPTS="compat=1.1"
 IMG_SIZE=$((64 * 1024 * 1024 + 512))
 
 echo
diff --git a/tests/qemu-iotests/068 b/tests/qemu-iotests/068
index c164ccc64a..fe9d7ae1be 100755
--- a/tests/qemu-iotests/068
+++ b/tests/qemu-iotests/068
@@ -39,8 +39,9 @@ trap "_cleanup; exit \$status" 0 1 2 3 15
 # This tests qcow2-specific low-level functionality
 _supported_fmt qcow2
 _supported_proto generic
+# Internal snapshots are (currently) impossible with refcount_bits=1
+_unsupported_imgopts 'compat=0.10' 'refcount_bits=1[^0-9]'
 
-IMGOPTS="compat=1.1"
 IMG_SIZE=128K
 
 case "$QEMU_DEFAULT_MACHINE" in
diff --git a/tests/qemu-iotests/098 b/tests/qemu-iotests/098
index 1c1d1c468f..700068b328 100755
--- a/tests/qemu-iotests/098
+++ b/tests/qemu-iotests/098
@@ -40,8 +40,8 @@ trap "_cleanup; exit \$status" 0 1 2 3 15
 
 _supported_fmt qcow2
 _supported_proto file
-
-IMGOPTS="compat=1.1"
+# The code path we want to test here only works for compat=1.1 images
+_unsupported_imgopts 'compat=0.10'
 
 for event in l1_update empty_image_prepare reftable_update refblock_alloc; do