diff --git a/qemu-img.c b/qemu-img.c
index 4a7ce43dc9..9b7506b8ae 100644
--- a/qemu-img.c
+++ b/qemu-img.c
@@ -2005,6 +2005,8 @@ static int convert_do_copy(ImgConvertState *s)
     return s->ret;
 }
 
+#define MAX_BUF_SECTORS 32768
+
 static int img_convert(int argc, char **argv)
 {
     int c, bs_i, flags, src_flags = 0;
@@ -2100,8 +2102,12 @@ static int img_convert(int argc, char **argv)
             int64_t sval;
 
             sval = cvtnum(optarg);
-            if (sval < 0) {
-                error_report("Invalid minimum zero buffer size for sparse output specified");
+            if (sval < 0 || sval & (BDRV_SECTOR_SIZE - 1) ||
+                sval / BDRV_SECTOR_SIZE > MAX_BUF_SECTORS) {
+                error_report("Invalid buffer size for sparse output specified. "
+                    "Valid sizes are multiples of %llu up to %llu. Select "
+                    "0 to disable sparse detection (fully allocates output).",
+                    BDRV_SECTOR_SIZE, MAX_BUF_SECTORS * BDRV_SECTOR_SIZE);
                 goto fail_getopt;
             }
 
@@ -2385,9 +2391,9 @@ static int img_convert(int argc, char **argv)
     }
 
     /* increase bufsectors from the default 4096 (2M) if opt_transfer
-     * or discard_alignment of the out_bs is greater. Limit to 32768 (16MB)
-     * as maximum. */
-    s.buf_sectors = MIN(32768,
+     * or discard_alignment of the out_bs is greater. Limit to
+     * MAX_BUF_SECTORS as maximum which is currently 32768 (16MB). */
+    s.buf_sectors = MIN(MAX_BUF_SECTORS,
                         MAX(s.buf_sectors,
                             MAX(out_bs->bl.opt_transfer >> BDRV_SECTOR_BITS,
                                 out_bs->bl.pdiscard_alignment >>