diff --git a/qemu-img.c b/qemu-img.c
index d806cfa193..070fe2e229 100644
--- a/qemu-img.c
+++ b/qemu-img.c
@@ -747,14 +747,20 @@ static int img_convert(int argc, char **argv)
                 n = bs_offset + bs_sectors - sector_num;
 
             if (strcmp(drv->format_name, "host_device")) {
-                if (!bdrv_is_allocated(bs[bs_i], sector_num - bs_offset,
-                                       n, &n1)) {
-                    sector_num += n1;
-                    continue;
+                /* If the output image is being created as a copy on write image,
+                   assume that sectors which are unallocated in the input image
+                   are present in both the output's and input's base images (no
+                   need to copy them). */
+                if (out_baseimg) {
+                    if (!bdrv_is_allocated(bs[bs_i], sector_num - bs_offset,
+                                           n, &n1)) {
+                        sector_num += n1;
+                        continue;
+                    }
+                    /* The next 'n1' sectors are allocated in the input image. Copy
+                       only those as they may be followed by unallocated sectors. */
+                    n = n1;
                 }
-                /* The next 'n1' sectors are allocated in the input image. Copy
-                   only those as they may be followed by unallocated sectors. */
-                n = n1;
             } else {
                 n1 = n;
             }