diff --git a/tests/qemu-iotests/271 b/tests/qemu-iotests/271
index e243f57ba7..59a6fafa2f 100755
--- a/tests/qemu-iotests/271
+++ b/tests/qemu-iotests/271
@@ -965,6 +965,71 @@ echo
 
 TEST_IMG="$TEST_IMG.top" alloc="1 30" zero="" _verify_l2_bitmap 0
 
+# Check that rebase with compression works correctly with images containing
+# subclusters.  When compression is enabled and we allocate a new
+# subcluster within the target (overlay) image, we expect the entire cluster
+# containing that subcluster to become compressed.
+#
+# Here we expect 1st and 3rd clusters of the top (overlay) image to become
+# compressed after the rebase, while cluster 2 to remain unallocated and
+# be read from the base (new backing) image.
+#
+# Base (new backing): |-- -- .. -- --|11 11 .. 11 11|-- -- .. -- --|
+# Mid (old backing):  |-- -- .. -- 22|-- -- .. -- --|33 -- .. -- --|
+# Top:                |-- -- .. -- --|-- -- -- -- --|-- -- .. -- --|
+
+echo
+echo "### Rebase with compression for images with subclusters ###"
+echo
+
+echo "# create backing chain"
+echo
+
+TEST_IMG="$TEST_IMG.base" _make_test_img -o cluster_size=1M,extended_l2=on 3M
+TEST_IMG="$TEST_IMG.mid" _make_test_img -o cluster_size=1M,extended_l2=on \
+    -b "$TEST_IMG.base" -F qcow2 3M
+TEST_IMG="$TEST_IMG.top" _make_test_img -o cluster_size=1M,extended_l2=on \
+    -b "$TEST_IMG.mid" -F qcow2 3M
+
+echo
+echo "# fill old and new backing with data"
+echo
+
+$QEMU_IO -c "write -P 0x11 1M 1M" "$TEST_IMG.base" | _filter_qemu_io
+$QEMU_IO -c "write -P 0x22 $(( 31 * 32 ))k 32k" \
+         -c "write -P 0x33 $(( 64 * 32 ))k 32k" \
+         "$TEST_IMG.mid" | _filter_qemu_io
+
+echo
+echo "# rebase topmost image onto the new backing, with compression"
+echo
+
+$QEMU_IMG rebase -c -b "$TEST_IMG.base" -F qcow2 "$TEST_IMG.top"
+
+echo "# verify that the 1st and 3rd clusters've become compressed"
+echo
+
+$QEMU_IMG map --output=json "$TEST_IMG.top" | _filter_testdir
+
+echo
+echo "# verify that data is read the same before and after rebase"
+echo
+
+$QEMU_IO -c "read -P 0x22 $(( 31 * 32 ))k 32k" \
+         -c "read -P 0x11 1M 1M" \
+         -c "read -P 0x33 $(( 64 * 32 ))k 32k" \
+         "$TEST_IMG.top" | _filter_qemu_io
+
+echo
+echo "# verify image bitmap"
+echo
+
+# For compressed clusters bitmap is always 0.  For unallocated cluster
+# there should be no entry at all, thus bitmap is also 0.
+TEST_IMG="$TEST_IMG.top" alloc="" zero="" _verify_l2_bitmap 0
+TEST_IMG="$TEST_IMG.top" alloc="" zero="" _verify_l2_bitmap 1
+TEST_IMG="$TEST_IMG.top" alloc="" zero="" _verify_l2_bitmap 2
+
 # success, all done
 echo "*** done"
 rm -f $seq.full
diff --git a/tests/qemu-iotests/271.out b/tests/qemu-iotests/271.out
index c335a6c608..0b24d50159 100644
--- a/tests/qemu-iotests/271.out
+++ b/tests/qemu-iotests/271.out
@@ -765,4 +765,44 @@ Offset          Length          Mapped to       File
 # verify image bitmap
 
 L2 entry #0: 0x8000000000500000 0000000040000002
+
+### Rebase with compression for images with subclusters ###
+
+# create backing chain
+
+Formatting 'TEST_DIR/t.IMGFMT.base', fmt=IMGFMT size=3145728
+Formatting 'TEST_DIR/t.IMGFMT.mid', fmt=IMGFMT size=3145728 backing_file=TEST_DIR/t.IMGFMT.base backing_fmt=IMGFMT
+Formatting 'TEST_DIR/t.IMGFMT.top', fmt=IMGFMT size=3145728 backing_file=TEST_DIR/t.IMGFMT.mid backing_fmt=IMGFMT
+
+# fill old and new backing with data
+
+wrote 1048576/1048576 bytes at offset 1048576
+1 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+wrote 32768/32768 bytes at offset 1015808
+32 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+wrote 32768/32768 bytes at offset 2097152
+32 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+
+# rebase topmost image onto the new backing, with compression
+
+# verify that the 1st and 3rd clusters've become compressed
+
+[{ "start": 0, "length": 1048576, "depth": 0, "present": true, "zero": false, "data": true, "compressed": true},
+{ "start": 1048576, "length": 1048576, "depth": 1, "present": true, "zero": false, "data": true, "compressed": false, "offset": 5242880},
+{ "start": 2097152, "length": 1048576, "depth": 0, "present": true, "zero": false, "data": true, "compressed": true}]
+
+# verify that data is read the same before and after rebase
+
+read 32768/32768 bytes at offset 1015808
+32 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 1048576/1048576 bytes at offset 1048576
+1 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 32768/32768 bytes at offset 2097152
+32 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+
+# verify image bitmap
+
+L2 entry #0: 0x4008000000500000 0000000000000000
+L2 entry #1: 0x0000000000000000 0000000000000000
+L2 entry #2: 0x400800000050040b 0000000000000000
 *** done
diff --git a/tests/qemu-iotests/314 b/tests/qemu-iotests/314
new file mode 100755
index 0000000000..96d7b4d258
--- /dev/null
+++ b/tests/qemu-iotests/314
@@ -0,0 +1,165 @@
+#!/usr/bin/env bash
+# group: rw backing auto quick
+#
+# Test qemu-img rebase with compression
+#
+# Copyright (c) 2023 Virtuozzo International GmbH.
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+#
+
+# creator
+owner=andrey.drobyshev@virtuozzo.com
+
+seq=`basename $0`
+echo "QA output created by $seq"
+
+status=1	# failure is the default!
+
+_cleanup()
+{
+    _cleanup_test_img
+    _rm_test_img "$TEST_IMG.base"
+    _rm_test_img "$TEST_IMG.itmd"
+}
+trap "_cleanup; exit \$status" 0 1 2 3 15
+
+# get standard environment, filters and checks
+. ./common.rc
+. ./common.filter
+
+_supported_fmt qcow2
+_supported_proto file
+_supported_os Linux
+
+# Want the size divisible by 2 and 3
+size=$(( 48 * 1024 * 1024 ))
+half_size=$(( size / 2 ))
+third_size=$(( size / 3 ))
+
+# 1. "qemu-img rebase -c" should refuse working with any format which doesn't
+# support compression.  We only check "-f raw" here.
+echo
+echo "=== Testing compressed rebase format compatibility ==="
+echo
+
+$QEMU_IMG create -f raw "$TEST_IMG" "$size" | _filter_img_create
+$QEMU_IMG rebase -c -f raw -b "" "$TEST_IMG"
+
+# 2. Write the 1st half of $size to backing file (compressed), 2nd half -- to
+# the top image (also compressed).  Rebase the top image onto no backing file,
+# with compression (i.e. "qemu-img -c -b ''").  Check that the resulting image
+# has the written data preserved, and "qemu-img check" reports 100% clusters
+# as compressed.
+echo
+echo "=== Testing rebase with compression onto no backing file ==="
+echo
+
+TEST_IMG="$TEST_IMG.base" _make_test_img $size
+_make_test_img -b "$TEST_IMG.base" -F $IMGFMT $size
+
+$QEMU_IO -c "write -c -P 0xaa 0 $half_size" "$TEST_IMG.base" | _filter_qemu_io
+$QEMU_IO -c "write -c -P 0xbb $half_size $half_size" "$TEST_IMG" \
+    | _filter_qemu_io
+
+$QEMU_IMG rebase -c -f $IMGFMT -b "" "$TEST_IMG"
+
+$QEMU_IO -c "read -P 0xaa 0 $half_size" "$TEST_IMG" | _filter_qemu_io
+$QEMU_IO -c "read -P 0xbb $half_size $half_size" "$TEST_IMG" | _filter_qemu_io
+
+$QEMU_IMG check "$TEST_IMG" | _filter_testdir
+
+# 3. Same as the previous one, but with raw backing file (hence write to
+# the backing is uncompressed).
+echo
+echo "=== Testing rebase with compression with raw backing file ==="
+echo
+
+$QEMU_IMG create -f raw "$TEST_IMG.base" "$half_size" | _filter_img_create
+_make_test_img -b "$TEST_IMG.base" -F raw $size
+
+$QEMU_IO -f raw -c "write -P 0xaa 0 $half_size" "$TEST_IMG.base" \
+    | _filter_qemu_io
+$QEMU_IO -c "write -c -P 0xbb $half_size $half_size" \
+    "$TEST_IMG" | _filter_qemu_io
+
+$QEMU_IMG rebase -c -f $IMGFMT -b "" "$TEST_IMG"
+
+$QEMU_IO -c "read -P 0xaa 0 $half_size" "$TEST_IMG" | _filter_qemu_io
+$QEMU_IO -c "read -P 0xbb $half_size $half_size" "$TEST_IMG" | _filter_qemu_io
+
+$QEMU_IMG check "$TEST_IMG" | _filter_testdir
+
+# 4. Create a backing chain base<--itmd<--img, filling 1st, 2nd and 3rd
+# thirds of them, respectively (with compression).  Rebase img onto base,
+# effectively deleting itmd from the chain, and check that written data is
+# preserved in the resulting image.  Also check that "qemu-img check" reports
+# 100% clusters as compressed.
+echo
+echo "=== Testing compressed rebase removing single delta from the chain ==="
+echo
+
+TEST_IMG="$TEST_IMG.base" _make_test_img $size
+TEST_IMG="$TEST_IMG.itmd" _make_test_img -b "$TEST_IMG.base" -F $IMGFMT $size
+_make_test_img -b "$TEST_IMG.itmd" -F $IMGFMT $size
+
+$QEMU_IO -c "write -c -P 0xaa 0 $third_size" \
+    "$TEST_IMG.base" | _filter_qemu_io
+$QEMU_IO -c "write -c -P 0xbb $third_size $third_size" \
+    "$TEST_IMG.itmd" | _filter_qemu_io
+$QEMU_IO -c "write -c -P 0xcc $((third_size * 2 )) $third_size" \
+    "$TEST_IMG" | _filter_qemu_io
+
+$QEMU_IMG rebase -c -f $IMGFMT -b "$TEST_IMG.base" -F $IMGFMT "$TEST_IMG"
+
+$QEMU_IO -c "read -P 0xaa 0 $third_size" "$TEST_IMG" | _filter_qemu_io
+$QEMU_IO -c "read -P 0xbb $third_size $third_size" \
+    "$TEST_IMG" | _filter_qemu_io
+$QEMU_IO -c "read -P 0xcc $(( third_size * 2 )) $third_size" \
+    "$TEST_IMG" | _filter_qemu_io
+
+$QEMU_IMG check "$TEST_IMG" | _filter_testdir
+
+# 5. Create one-cluster backing and overlay images, and fill only the first
+# (half - 1) bytes of the backing with data (uncompressed).  Rebase the
+# overlay onto no backing file with compression.  Check that data is still
+# read correctly, and that cluster is now really compressed ("qemu-img check"
+# reports 100% clusters as compressed.
+echo
+echo "=== Testing compressed rebase with unaligned unmerged data ==="
+echo
+
+CLUSTER_SIZE=65536
+
+TEST_IMG="$TEST_IMG.base" _make_test_img $CLUSTER_SIZE
+_make_test_img -b "$TEST_IMG.base" -F $IMGFMT $CLUSTER_SIZE
+
+$QEMU_IO -c "write -P 0xaa 0 $(( CLUSTER_SIZE / 2 - 1 ))" $TEST_IMG.base \
+    | _filter_qemu_io
+
+$QEMU_IMG rebase -c -f $IMGFMT -b "" "$TEST_IMG"
+
+$QEMU_IO -c "read -P 0xaa 0 $(( CLUSTER_SIZE / 2 - 1 ))" "$TEST_IMG" \
+    | _filter_qemu_io
+$QEMU_IO -c \
+    "read -P 0x00 $(( CLUSTER_SIZE / 2 - 1 )) $(( CLUSTER_SIZE / 2 + 1 ))" \
+    "$TEST_IMG" | _filter_qemu_io
+
+$QEMU_IMG check "$TEST_IMG" | _filter_testdir
+
+# success, all done
+echo
+echo '*** done'
+rm -f $seq.full
+status=0
diff --git a/tests/qemu-iotests/314.out b/tests/qemu-iotests/314.out
new file mode 100644
index 0000000000..ac9337a543
--- /dev/null
+++ b/tests/qemu-iotests/314.out
@@ -0,0 +1,75 @@
+QA output created by 314
+
+=== Testing compressed rebase format compatibility ===
+
+Formatting 'TEST_DIR/t.IMGFMT', fmt=raw size=50331648
+qemu-img: Compression not supported for this file format
+
+=== Testing rebase with compression onto no backing file ===
+
+Formatting 'TEST_DIR/t.IMGFMT.base', fmt=IMGFMT size=50331648
+Formatting 'TEST_DIR/t.IMGFMT', fmt=IMGFMT size=50331648 backing_file=TEST_DIR/t.IMGFMT.base backing_fmt=IMGFMT
+wrote 25165824/25165824 bytes at offset 0
+24 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+wrote 25165824/25165824 bytes at offset 25165824
+24 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 25165824/25165824 bytes at offset 0
+24 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 25165824/25165824 bytes at offset 25165824
+24 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+No errors were found on the image.
+768/768 = 100.00% allocated, 100.00% fragmented, 100.00% compressed clusters
+Image end offset: 458752
+
+=== Testing rebase with compression with raw backing file ===
+
+Formatting 'TEST_DIR/t.IMGFMT.base', fmt=raw size=25165824
+Formatting 'TEST_DIR/t.IMGFMT', fmt=IMGFMT size=50331648 backing_file=TEST_DIR/t.IMGFMT.base backing_fmt=raw
+wrote 25165824/25165824 bytes at offset 0
+24 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+wrote 25165824/25165824 bytes at offset 25165824
+24 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 25165824/25165824 bytes at offset 0
+24 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 25165824/25165824 bytes at offset 25165824
+24 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+No errors were found on the image.
+768/768 = 100.00% allocated, 100.00% fragmented, 100.00% compressed clusters
+Image end offset: 458752
+
+=== Testing compressed rebase removing single delta from the chain ===
+
+Formatting 'TEST_DIR/t.IMGFMT.base', fmt=IMGFMT size=50331648
+Formatting 'TEST_DIR/t.IMGFMT.itmd', fmt=IMGFMT size=50331648 backing_file=TEST_DIR/t.IMGFMT.base backing_fmt=IMGFMT
+Formatting 'TEST_DIR/t.IMGFMT', fmt=IMGFMT size=50331648 backing_file=TEST_DIR/t.IMGFMT.itmd backing_fmt=IMGFMT
+wrote 16777216/16777216 bytes at offset 0
+16 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+wrote 16777216/16777216 bytes at offset 16777216
+16 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+wrote 16777216/16777216 bytes at offset 33554432
+16 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 16777216/16777216 bytes at offset 0
+16 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 16777216/16777216 bytes at offset 16777216
+16 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 16777216/16777216 bytes at offset 33554432
+16 MiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+No errors were found on the image.
+512/768 = 66.67% allocated, 100.00% fragmented, 100.00% compressed clusters
+Image end offset: 458752
+
+=== Testing compressed rebase with unaligned unmerged data ===
+
+Formatting 'TEST_DIR/t.IMGFMT.base', fmt=IMGFMT size=65536
+Formatting 'TEST_DIR/t.IMGFMT', fmt=IMGFMT size=65536 backing_file=TEST_DIR/t.IMGFMT.base backing_fmt=IMGFMT
+wrote 32767/32767 bytes at offset 0
+31.999 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 32767/32767 bytes at offset 0
+31.999 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 32769/32769 bytes at offset 32767
+32.001 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+No errors were found on the image.
+1/1 = 100.00% allocated, 100.00% fragmented, 100.00% compressed clusters
+Image end offset: 393216
+
+*** done