diff --git a/block/qcow2.c b/block/qcow2.c
index 2bb536b..e8cbcc1 100644
--- a/block/qcow2.c
+++ b/block/qcow2.c
@@ -3784,6 +3784,12 @@
     int ret;
     BDRVQcow2State *s = bs->opaque;
 
+    /* If the image does not support QCOW_OFLAG_ZERO then discarding
+     * clusters could expose stale data from the backing file. */
+    if (s->qcow_version < 3 && bs->backing) {
+        return -ENOTSUP;
+    }
+
     if (!QEMU_IS_ALIGNED(offset | bytes, s->cluster_size)) {
         assert(bytes < s->cluster_size);
         /* Ignore partial clusters, except for the special case of the
diff --git a/tests/qemu-iotests/046 b/tests/qemu-iotests/046
index a066eec..ecbe5fc 100755
--- a/tests/qemu-iotests/046
+++ b/tests/qemu-iotests/046
@@ -193,8 +193,8 @@
 verify_io()
 {
     if ($QEMU_IMG info -U -f "$IMGFMT" "$TEST_IMG" | grep "compat: 0.10" > /dev/null); then
-        # For v2 images, discarded clusters are read from the backing file
-        # Keep the variable empty so that the backing file value can be used as
+        # In v2 images clusters are not discarded when there is a backing file.
+        # Keep the variable empty so that the previous value can be used as
         # the default below
         discarded=
     else
@@ -230,14 +230,16 @@
     echo read -P 70 0x78000 0x6000
     echo read -P 7  0x7e000 0x2000
 
-    echo read -P ${discarded:-8} 0x80000 0x6000
+    echo read -P ${discarded:-89} 0x80000 0x1000
+    echo read -P ${discarded:-8} 0x81000 0x5000
     echo read -P 80 0x86000 0x2000
     echo read -P ${discarded:-8} 0x88000 0x2000
     echo read -P 81 0x8a000 0xe000
     echo read -P 90 0x98000 0x6000
     echo read -P 9  0x9e000 0x2000
 
-    echo read -P ${discarded:-10} 0xa0000 0x6000
+    echo read -P ${discarded:-109} 0xa0000 0x1000
+    echo read -P ${discarded:-10} 0xa1000 0x5000
     echo read -P 100 0xa6000 0x2000
     echo read -P ${discarded:-10} 0xa8000 0x2000
     echo read -P 101 0xaa000 0xe000
diff --git a/tests/qemu-iotests/046.out b/tests/qemu-iotests/046.out
index ca2c740..7078304 100644
--- a/tests/qemu-iotests/046.out
+++ b/tests/qemu-iotests/046.out
@@ -187,8 +187,10 @@
 24 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
 read 8192/8192 bytes at offset 516096
 8 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
-read 24576/24576 bytes at offset 524288
-24 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 4096/4096 bytes at offset 524288
+4 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 20480/20480 bytes at offset 528384
+20 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
 read 8192/8192 bytes at offset 548864
 8 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
 read 8192/8192 bytes at offset 557056
@@ -199,8 +201,10 @@
 24 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
 read 8192/8192 bytes at offset 647168
 8 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
-read 24576/24576 bytes at offset 655360
-24 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 4096/4096 bytes at offset 655360
+4 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+read 20480/20480 bytes at offset 659456
+20 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
 read 8192/8192 bytes at offset 679936
 8 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
 read 8192/8192 bytes at offset 688128
diff --git a/tests/qemu-iotests/060 b/tests/qemu-iotests/060
index 043f129..32c0ecc 100755
--- a/tests/qemu-iotests/060
+++ b/tests/qemu-iotests/060
@@ -160,18 +160,16 @@
 
 $QEMU_IO -c 'write 0k 64k' "$BACKING_IMG" | _filter_qemu_io
 
-# compat=0.10 is required in order to make the following discard actually
-# unallocate the sector rather than make it a zero sector - we want COW, after
-# all.
-_make_test_img -o 'compat=0.10' -b "$BACKING_IMG" 1G
+_make_test_img -b "$BACKING_IMG" 1G
 # Write two clusters, the second one enforces creation of an L2 table after
 # the first data cluster.
 $QEMU_IO -c 'write 0k 64k' -c 'write 512M 64k' "$TEST_IMG" | _filter_qemu_io
-# Discard the first cluster. This cluster will soon enough be reallocated and
+# Free the first cluster. This cluster will soon enough be reallocated and
 # used for COW.
-$QEMU_IO -c 'discard 0k 64k' "$TEST_IMG" | _filter_qemu_io
+poke_file "$TEST_IMG" "$l2_offset" "\x00\x00\x00\x00\x00\x00\x00\x00"
+poke_file "$TEST_IMG" "$(($rb_offset+10))" "\x00\x00"
 # Now, corrupt the image by marking the second L2 table cluster as free.
-poke_file "$TEST_IMG" '131084' "\x00\x00" # 0x2000c
+poke_file "$TEST_IMG" "$(($rb_offset+12))" "\x00\x00"
 # Start a write operation requiring COW on the image stopping it right before
 # doing the read; then, trigger the corruption prevention by writing anything to
 # any unallocated cluster, leading to an attempt to overwrite the second L2
diff --git a/tests/qemu-iotests/060.out b/tests/qemu-iotests/060.out
index d27692a..09caaea 100644
--- a/tests/qemu-iotests/060.out
+++ b/tests/qemu-iotests/060.out
@@ -105,8 +105,6 @@
 64 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
 wrote 65536/65536 bytes at offset 536870912
 64 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
-discard 65536/65536 bytes at offset 0
-64 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
 qcow2: Marking image as corrupt: Preventing invalid write on metadata (overlaps with active L2 table); further corruption events will be suppressed
 blkdebug: Suspended request '0'
 write failed: Input/output error
diff --git a/tests/qemu-iotests/177 b/tests/qemu-iotests/177
index 752d29f..eadc2c7 100755
--- a/tests/qemu-iotests/177
+++ b/tests/qemu-iotests/177
@@ -89,8 +89,9 @@
 {
     if ($QEMU_IMG info -f "$IMGFMT" "$TEST_IMG" |
 	    grep "compat: 0.10" > /dev/null); then
-        # For v2 images, discarded clusters are read from the backing file
-        discarded=11
+        # In v2 images clusters are not discarded when there is a backing file
+        # so the previous value is read
+        discarded=22
     else
         # Discarded clusters are zeroed for v3 or later
         discarded=0
diff --git a/tests/qemu-iotests/290 b/tests/qemu-iotests/290
new file mode 100755
index 0000000..776b65e
--- /dev/null
+++ b/tests/qemu-iotests/290
@@ -0,0 +1,97 @@
+#!/usr/bin/env bash
+#
+# Test how 'qemu-io -c discard' behaves on v2 and v3 qcow2 images
+#
+# Copyright (C) 2020 Igalia, S.L.
+# Author: Alberto Garcia <berto@igalia.com>
+#
+# 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=berto@igalia.com
+
+seq=`basename $0`
+echo "QA output created by $seq"
+
+status=1    # failure is the default!
+
+_cleanup()
+{
+    _cleanup_test_img
+}
+trap "_cleanup; exit \$status" 0 1 2 3 15
+
+# get standard environment, filters and checks
+. ./common.rc
+. ./common.filter
+
+_supported_fmt qcow2
+_supported_proto file
+_supported_os Linux
+_unsupported_imgopts 'compat=0.10' refcount_bits data_file
+
+echo
+echo "### Test 'qemu-io -c discard' on a QCOW2 image without a backing file"
+echo
+for qcow2_compat in 0.10 1.1; do
+    echo "# Create an image with compat=$qcow2_compat without a backing file"
+    _make_test_img -o "compat=$qcow2_compat" 128k
+
+    echo "# Fill all clusters with data and then discard them"
+    $QEMU_IO -c 'write -P 0x01 0 128k' "$TEST_IMG" | _filter_qemu_io
+    $QEMU_IO -c 'discard 0 128k' "$TEST_IMG" | _filter_qemu_io
+
+    echo "# Read the data from the discarded clusters"
+    $QEMU_IO -c 'read -P 0x00 0 128k' "$TEST_IMG" | _filter_qemu_io
+
+    echo "# Output of qemu-img map"
+    $QEMU_IMG map "$TEST_IMG" | _filter_testdir
+done
+
+echo
+echo "### Test 'qemu-io -c discard' on a QCOW2 image with a backing file"
+echo
+
+echo "# Create a backing image and fill it with data"
+BACKING_IMG="$TEST_IMG.base"
+TEST_IMG="$BACKING_IMG" _make_test_img 128k
+$QEMU_IO -c 'write -P 0xff 0 128k' "$BACKING_IMG" | _filter_qemu_io
+
+for qcow2_compat in 0.10 1.1; do
+    echo "# Create an image with compat=$qcow2_compat and a backing file"
+    _make_test_img -o "compat=$qcow2_compat" -b "$BACKING_IMG"
+
+    echo "# Fill all clusters with data and then discard them"
+    $QEMU_IO -c 'write -P 0x01 0 128k' "$TEST_IMG" | _filter_qemu_io
+    $QEMU_IO -c 'discard 0 128k' "$TEST_IMG" | _filter_qemu_io
+
+    echo "# Read the data from the discarded clusters"
+    if [ "$qcow2_compat" = "1.1" ]; then
+        # In qcow2 v3 clusters are zeroed (with QCOW_OFLAG_ZERO)
+        $QEMU_IO -c 'read -P 0x00 0 128k' "$TEST_IMG" | _filter_qemu_io
+    else
+        # In qcow2 v2 if there's a backing image we cannot zero the clusters
+        # without exposing the backing file data so discard does nothing
+        $QEMU_IO -c 'read -P 0x01 0 128k' "$TEST_IMG" | _filter_qemu_io
+    fi
+
+    echo "# Output of qemu-img map"
+    $QEMU_IMG map "$TEST_IMG" | _filter_testdir
+done
+
+# success, all done
+echo "*** done"
+rm -f $seq.full
+status=0
diff --git a/tests/qemu-iotests/290.out b/tests/qemu-iotests/290.out
new file mode 100644
index 0000000..d2259c8
--- /dev/null
+++ b/tests/qemu-iotests/290.out
@@ -0,0 +1,61 @@
+QA output created by 290
+
+### Test 'qemu-io -c discard' on a QCOW2 image without a backing file
+
+# Create an image with compat=0.10 without a backing file
+Formatting 'TEST_DIR/t.IMGFMT', fmt=IMGFMT size=131072
+# Fill all clusters with data and then discard them
+wrote 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+discard 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+# Read the data from the discarded clusters
+read 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+# Output of qemu-img map
+Offset          Length          Mapped to       File
+# Create an image with compat=1.1 without a backing file
+Formatting 'TEST_DIR/t.IMGFMT', fmt=IMGFMT size=131072
+# Fill all clusters with data and then discard them
+wrote 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+discard 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+# Read the data from the discarded clusters
+read 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+# Output of qemu-img map
+Offset          Length          Mapped to       File
+
+### Test 'qemu-io -c discard' on a QCOW2 image with a backing file
+
+# Create a backing image and fill it with data
+Formatting 'TEST_DIR/t.IMGFMT.base', fmt=IMGFMT size=131072
+wrote 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+# Create an image with compat=0.10 and a backing file
+Formatting 'TEST_DIR/t.IMGFMT', fmt=IMGFMT size=131072 backing_file=TEST_DIR/t.IMGFMT.base
+# Fill all clusters with data and then discard them
+wrote 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+discard 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+# Read the data from the discarded clusters
+read 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+# Output of qemu-img map
+Offset          Length          Mapped to       File
+0               0x20000         0x50000         TEST_DIR/t.qcow2
+# Create an image with compat=1.1 and a backing file
+Formatting 'TEST_DIR/t.IMGFMT', fmt=IMGFMT size=131072 backing_file=TEST_DIR/t.IMGFMT.base
+# Fill all clusters with data and then discard them
+wrote 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+discard 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+# Read the data from the discarded clusters
+read 131072/131072 bytes at offset 0
+128 KiB, X ops; XX:XX:XX.X (XXX YYY/sec and XXX ops/sec)
+# Output of qemu-img map
+Offset          Length          Mapped to       File
+*** done
diff --git a/tests/qemu-iotests/group b/tests/qemu-iotests/group
index 79c6dfc..435dccd 100644
--- a/tests/qemu-iotests/group
+++ b/tests/qemu-iotests/group
@@ -296,3 +296,4 @@
 286 rw quick
 288 quick
 289 rw quick
+290 rw auto quick