diff --git a/qemu-img.c b/qemu-img.c
index 9dddfbefce..8d30e43b53 100644
--- a/qemu-img.c
+++ b/qemu-img.c
@@ -1305,20 +1305,312 @@ out3:
     return ret;
 }
 
+enum ImgConvertBlockStatus {
+    BLK_DATA,
+    BLK_ZERO,
+    BLK_BACKING_FILE,
+};
+
+typedef struct ImgConvertState {
+    BlockBackend **src;
+    int64_t *src_sectors;
+    int src_cur, src_num;
+    int64_t src_cur_offset;
+    int64_t total_sectors;
+    int64_t allocated_sectors;
+    enum ImgConvertBlockStatus status;
+    int64_t sector_next_status;
+    BlockBackend *target;
+    bool has_zero_init;
+    bool compressed;
+    bool target_has_backing;
+    int min_sparse;
+    size_t cluster_sectors;
+    size_t buf_sectors;
+} ImgConvertState;
+
+static void convert_select_part(ImgConvertState *s, int64_t sector_num)
+{
+    assert(sector_num >= s->src_cur_offset);
+    while (sector_num - s->src_cur_offset >= s->src_sectors[s->src_cur]) {
+        s->src_cur_offset += s->src_sectors[s->src_cur];
+        s->src_cur++;
+        assert(s->src_cur < s->src_num);
+    }
+}
+
+static int convert_iteration_sectors(ImgConvertState *s, int64_t sector_num)
+{
+    int64_t ret;
+    int n;
+
+    convert_select_part(s, sector_num);
+
+    assert(s->total_sectors > sector_num);
+    n = MIN(s->total_sectors - sector_num, BDRV_REQUEST_MAX_SECTORS);
+
+    if (s->sector_next_status <= sector_num) {
+        ret = bdrv_get_block_status(blk_bs(s->src[s->src_cur]),
+                                    sector_num - s->src_cur_offset,
+                                    n, &n);
+        if (ret < 0) {
+            return ret;
+        }
+
+        if (ret & BDRV_BLOCK_ZERO) {
+            s->status = BLK_ZERO;
+        } else if (ret & BDRV_BLOCK_DATA) {
+            s->status = BLK_DATA;
+        } else if (!s->target_has_backing) {
+            /* Without a target backing file we must copy over the contents of
+             * the backing file as well. */
+            /* TODO Check block status of the backing file chain to avoid
+             * needlessly reading zeroes and limiting the iteration to the
+             * buffer size */
+            s->status = BLK_DATA;
+        } else {
+            s->status = BLK_BACKING_FILE;
+        }
+
+        s->sector_next_status = sector_num + n;
+    }
+
+    n = MIN(n, s->sector_next_status - sector_num);
+    if (s->status == BLK_DATA) {
+        n = MIN(n, s->buf_sectors);
+    }
+
+    /* We need to write complete clusters for compressed images, so if an
+     * unallocated area is shorter than that, we must consider the whole
+     * cluster allocated. */
+    if (s->compressed) {
+        if (n < s->cluster_sectors) {
+            n = MIN(s->cluster_sectors, s->total_sectors - sector_num);
+            s->status = BLK_DATA;
+        } else {
+            n = QEMU_ALIGN_DOWN(n, s->cluster_sectors);
+        }
+    }
+
+    return n;
+}
+
+static int convert_read(ImgConvertState *s, int64_t sector_num, int nb_sectors,
+                        uint8_t *buf)
+{
+    int n;
+    int ret;
+
+    if (s->status == BLK_ZERO || s->status == BLK_BACKING_FILE) {
+        return 0;
+    }
+
+    assert(nb_sectors <= s->buf_sectors);
+    while (nb_sectors > 0) {
+        BlockBackend *blk;
+        int64_t bs_sectors;
+
+        /* In the case of compression with multiple source files, we can get a
+         * nb_sectors that spreads into the next part. So we must be able to
+         * read across multiple BDSes for one convert_read() call. */
+        convert_select_part(s, sector_num);
+        blk = s->src[s->src_cur];
+        bs_sectors = s->src_sectors[s->src_cur];
+
+        n = MIN(nb_sectors, bs_sectors - (sector_num - s->src_cur_offset));
+        ret = blk_read(blk, sector_num - s->src_cur_offset, buf, n);
+        if (ret < 0) {
+            return ret;
+        }
+
+        sector_num += n;
+        nb_sectors -= n;
+        buf += n * BDRV_SECTOR_SIZE;
+    }
+
+    return 0;
+}
+
+static int convert_write(ImgConvertState *s, int64_t sector_num, int nb_sectors,
+                         const uint8_t *buf)
+{
+    int ret;
+
+    while (nb_sectors > 0) {
+        int n = nb_sectors;
+
+        switch (s->status) {
+        case BLK_BACKING_FILE:
+            /* If we have a backing file, leave clusters unallocated that are
+             * unallocated in the source image, so that the backing file is
+             * visible at the respective offset. */
+            assert(s->target_has_backing);
+            break;
+
+        case BLK_DATA:
+            /* We must always write compressed clusters as a whole, so don't
+             * try to find zeroed parts in the buffer. We can only save the
+             * write if the buffer is completely zeroed and we're allowed to
+             * keep the target sparse. */
+            if (s->compressed) {
+                if (s->has_zero_init && s->min_sparse &&
+                    buffer_is_zero(buf, n * BDRV_SECTOR_SIZE))
+                {
+                    assert(!s->target_has_backing);
+                    break;
+                }
+
+                ret = blk_write_compressed(s->target, sector_num, buf, n);
+                if (ret < 0) {
+                    return ret;
+                }
+                break;
+            }
+
+            /* If there is real non-zero data or we're told to keep the target
+             * fully allocated (-S 0), we must write it. Otherwise we can treat
+             * it as zero sectors. */
+            if (!s->min_sparse ||
+                is_allocated_sectors_min(buf, n, &n, s->min_sparse))
+            {
+                ret = blk_write(s->target, sector_num, buf, n);
+                if (ret < 0) {
+                    return ret;
+                }
+                break;
+            }
+            /* fall-through */
+
+        case BLK_ZERO:
+            if (s->has_zero_init) {
+                break;
+            }
+            ret = blk_write_zeroes(s->target, sector_num, n, 0);
+            if (ret < 0) {
+                return ret;
+            }
+            break;
+        }
+
+        sector_num += n;
+        nb_sectors -= n;
+        buf += n * BDRV_SECTOR_SIZE;
+    }
+
+    return 0;
+}
+
+static int convert_do_copy(ImgConvertState *s)
+{
+    uint8_t *buf = NULL;
+    int64_t sector_num, allocated_done;
+    int ret;
+    int n;
+
+    /* Check whether we have zero initialisation or can get it efficiently */
+    s->has_zero_init = s->min_sparse && !s->target_has_backing
+                     ? bdrv_has_zero_init(blk_bs(s->target))
+                     : false;
+
+    if (!s->has_zero_init && !s->target_has_backing &&
+        bdrv_can_write_zeroes_with_unmap(blk_bs(s->target)))
+    {
+        ret = bdrv_make_zero(blk_bs(s->target), BDRV_REQ_MAY_UNMAP);
+        if (ret == 0) {
+            s->has_zero_init = true;
+        }
+    }
+
+    /* Allocate buffer for copied data. For compressed images, only one cluster
+     * can be copied at a time. */
+    if (s->compressed) {
+        if (s->cluster_sectors <= 0 || s->cluster_sectors > s->buf_sectors) {
+            error_report("invalid cluster size");
+            ret = -EINVAL;
+            goto fail;
+        }
+        s->buf_sectors = s->cluster_sectors;
+    }
+    buf = blk_blockalign(s->target, s->buf_sectors * BDRV_SECTOR_SIZE);
+
+    /* Calculate allocated sectors for progress */
+    s->allocated_sectors = 0;
+    sector_num = 0;
+    while (sector_num < s->total_sectors) {
+        n = convert_iteration_sectors(s, sector_num);
+        if (n < 0) {
+            ret = n;
+            goto fail;
+        }
+        if (s->status == BLK_DATA) {
+            s->allocated_sectors += n;
+        }
+        sector_num += n;
+    }
+
+    /* Do the copy */
+    s->src_cur = 0;
+    s->src_cur_offset = 0;
+    s->sector_next_status = 0;
+
+    sector_num = 0;
+    allocated_done = 0;
+
+    while (sector_num < s->total_sectors) {
+        n = convert_iteration_sectors(s, sector_num);
+        if (n < 0) {
+            ret = n;
+            goto fail;
+        }
+        if (s->status == BLK_DATA) {
+            allocated_done += n;
+            qemu_progress_print(100.0 * allocated_done / s->allocated_sectors,
+                                0);
+        }
+
+        ret = convert_read(s, sector_num, n, buf);
+        if (ret < 0) {
+            error_report("error while reading sector %" PRId64
+                         ": %s", sector_num, strerror(-ret));
+            goto fail;
+        }
+
+        ret = convert_write(s, sector_num, n, buf);
+        if (ret < 0) {
+            error_report("error while writing sector %" PRId64
+                         ": %s", sector_num, strerror(-ret));
+            goto fail;
+        }
+
+        sector_num += n;
+    }
+
+    if (s->compressed) {
+        /* signal EOF to align */
+        ret = blk_write_compressed(s->target, 0, NULL, 0);
+        if (ret < 0) {
+            goto fail;
+        }
+    }
+
+    ret = 0;
+fail:
+    qemu_vfree(buf);
+    return ret;
+}
+
 static int img_convert(int argc, char **argv)
 {
-    int c, n, n1, bs_n, bs_i, compress, cluster_sectors, skip_create;
+    int c, bs_n, bs_i, compress, cluster_sectors, skip_create;
     int64_t ret = 0;
     int progress = 0, flags, src_flags;
     const char *fmt, *out_fmt, *cache, *src_cache, *out_baseimg, *out_filename;
     BlockDriver *drv, *proto_drv;
     BlockBackend **blk = NULL, *out_blk = NULL;
     BlockDriverState **bs = NULL, *out_bs = NULL;
-    int64_t total_sectors, nb_sectors, sector_num, bs_offset;
+    int64_t total_sectors;
     int64_t *bs_sectors = NULL;
-    uint8_t * buf = NULL;
     size_t bufsectors = IO_BUF_SIZE / BDRV_SECTOR_SIZE;
-    const uint8_t *buf1;
     BlockDriverInfo bdi;
     QemuOpts *opts = NULL;
     QemuOptsList *create_opts = NULL;
@@ -1329,6 +1621,7 @@ static int img_convert(int argc, char **argv)
     bool quiet = false;
     Error *local_err = NULL;
     QemuOpts *sn_opts = NULL;
+    ImgConvertState state;
 
     fmt = NULL;
     out_fmt = "raw";
@@ -1627,9 +1920,6 @@ static int img_convert(int argc, char **argv)
     }
     out_bs = blk_bs(out_blk);
 
-    bs_i = 0;
-    bs_offset = 0;
-
     /* increase bufsectors from the default 4096 (2M) if opt_transfer_length
      * or discard_alignment of the out_bs is greater. Limit to 32768 (16MB)
      * as maximum. */
@@ -1638,8 +1928,6 @@ static int img_convert(int argc, char **argv)
                                          out_bs->bl.discard_alignment))
                     );
 
-    buf = blk_blockalign(out_blk, bufsectors * BDRV_SECTOR_SIZE);
-
     if (skip_create) {
         int64_t output_sectors = blk_nb_sectors(out_blk);
         if (output_sectors < 0) {
@@ -1666,203 +1954,20 @@ static int img_convert(int argc, char **argv)
         cluster_sectors = bdi.cluster_size / BDRV_SECTOR_SIZE;
     }
 
-    if (compress) {
-        if (cluster_sectors <= 0 || cluster_sectors > bufsectors) {
-            error_report("invalid cluster size");
-            ret = -1;
-            goto out;
-        }
-        sector_num = 0;
+    state = (ImgConvertState) {
+        .src                = blk,
+        .src_sectors        = bs_sectors,
+        .src_num            = bs_n,
+        .total_sectors      = total_sectors,
+        .target             = out_blk,
+        .compressed         = compress,
+        .target_has_backing = (bool) out_baseimg,
+        .min_sparse         = min_sparse,
+        .cluster_sectors    = cluster_sectors,
+        .buf_sectors        = bufsectors,
+    };
+    ret = convert_do_copy(&state);
 
-        nb_sectors = total_sectors;
-
-        for(;;) {
-            int64_t bs_num;
-            int remainder;
-            uint8_t *buf2;
-
-            nb_sectors = total_sectors - sector_num;
-            if (nb_sectors <= 0)
-                break;
-            if (nb_sectors >= cluster_sectors)
-                n = cluster_sectors;
-            else
-                n = nb_sectors;
-
-            bs_num = sector_num - bs_offset;
-            assert (bs_num >= 0);
-            remainder = n;
-            buf2 = buf;
-            while (remainder > 0) {
-                int nlow;
-                while (bs_num == bs_sectors[bs_i]) {
-                    bs_offset += bs_sectors[bs_i];
-                    bs_i++;
-                    assert (bs_i < bs_n);
-                    bs_num = 0;
-                    /* printf("changing part: sector_num=%" PRId64 ", "
-                       "bs_i=%d, bs_offset=%" PRId64 ", bs_sectors=%" PRId64
-                       "\n", sector_num, bs_i, bs_offset, bs_sectors[bs_i]); */
-                }
-                assert (bs_num < bs_sectors[bs_i]);
-
-                nlow = remainder > bs_sectors[bs_i] - bs_num
-                    ? bs_sectors[bs_i] - bs_num : remainder;
-
-                ret = blk_read(blk[bs_i], bs_num, buf2, nlow);
-                if (ret < 0) {
-                    error_report("error while reading sector %" PRId64 ": %s",
-                                 bs_num, strerror(-ret));
-                    goto out;
-                }
-
-                buf2 += nlow * 512;
-                bs_num += nlow;
-
-                remainder -= nlow;
-            }
-            assert (remainder == 0);
-
-            if (!buffer_is_zero(buf, n * BDRV_SECTOR_SIZE)) {
-                ret = blk_write_compressed(out_blk, sector_num, buf, n);
-                if (ret != 0) {
-                    error_report("error while compressing sector %" PRId64
-                                 ": %s", sector_num, strerror(-ret));
-                    goto out;
-                }
-            }
-            sector_num += n;
-            qemu_progress_print(100.0 * sector_num / total_sectors, 0);
-        }
-        /* signal EOF to align */
-        blk_write_compressed(out_blk, 0, NULL, 0);
-    } else {
-        int64_t sectors_to_read, sectors_read, sector_num_next_status;
-        bool count_allocated_sectors;
-        int has_zero_init = min_sparse ? bdrv_has_zero_init(out_bs) : 0;
-
-        if (!has_zero_init && bdrv_can_write_zeroes_with_unmap(out_bs)) {
-            ret = bdrv_make_zero(out_bs, BDRV_REQ_MAY_UNMAP);
-            if (ret < 0) {
-                goto out;
-            }
-            has_zero_init = 1;
-        }
-
-        sectors_to_read = total_sectors;
-        count_allocated_sectors = progress && (out_baseimg || has_zero_init);
-restart:
-        sector_num = 0; // total number of sectors converted so far
-        sectors_read = 0;
-        sector_num_next_status = 0;
-
-        for(;;) {
-            nb_sectors = total_sectors - sector_num;
-            if (nb_sectors <= 0) {
-                if (count_allocated_sectors) {
-                    sectors_to_read = sectors_read;
-                    count_allocated_sectors = false;
-                    goto restart;
-                }
-                ret = 0;
-                break;
-            }
-
-            while (sector_num - bs_offset >= bs_sectors[bs_i]) {
-                bs_offset += bs_sectors[bs_i];
-                bs_i ++;
-                assert (bs_i < bs_n);
-                /* printf("changing part: sector_num=%" PRId64 ", bs_i=%d, "
-                  "bs_offset=%" PRId64 ", bs_sectors=%" PRId64 "\n",
-                   sector_num, bs_i, bs_offset, bs_sectors[bs_i]); */
-            }
-
-            if ((out_baseimg || has_zero_init) &&
-                sector_num >= sector_num_next_status) {
-                n = nb_sectors > INT_MAX ? INT_MAX : nb_sectors;
-                ret = bdrv_get_block_status(bs[bs_i], sector_num - bs_offset,
-                                            n, &n1);
-                if (ret < 0) {
-                    error_report("error while reading block status of sector %"
-                                 PRId64 ": %s", sector_num - bs_offset,
-                                 strerror(-ret));
-                    goto out;
-                }
-                /* If the output image is zero initialized, we are not working
-                 * on a shared base and the input is zero we can skip the next
-                 * n1 sectors */
-                if (has_zero_init && !out_baseimg && (ret & BDRV_BLOCK_ZERO)) {
-                    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 (!(ret & BDRV_BLOCK_DATA)) {
-                        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. */
-                    nb_sectors = n1;
-                }
-                /* avoid redundant callouts to get_block_status */
-                sector_num_next_status = sector_num + n1;
-            }
-
-            n = MIN(nb_sectors, bufsectors);
-
-            /* round down request length to an aligned sector, but
-             * do not bother doing this on short requests. They happen
-             * when we found an all-zero area, and the next sector to
-             * write will not be sector_num + n. */
-            if (cluster_sectors > 0 && n >= cluster_sectors) {
-                int64_t next_aligned_sector = (sector_num + n);
-                next_aligned_sector -= next_aligned_sector % cluster_sectors;
-                if (sector_num + n > next_aligned_sector) {
-                    n = next_aligned_sector - sector_num;
-                }
-            }
-
-            n = MIN(n, bs_sectors[bs_i] - (sector_num - bs_offset));
-
-            sectors_read += n;
-            if (count_allocated_sectors) {
-                sector_num += n;
-                continue;
-            }
-
-            n1 = n;
-            ret = blk_read(blk[bs_i], sector_num - bs_offset, buf, n);
-            if (ret < 0) {
-                error_report("error while reading sector %" PRId64 ": %s",
-                             sector_num - bs_offset, strerror(-ret));
-                goto out;
-            }
-            /* NOTE: at the same time we convert, we do not write zero
-               sectors to have a chance to compress the image. Ideally, we
-               should add a specific call to have the info to go faster */
-            buf1 = buf;
-            while (n > 0) {
-                if (!has_zero_init ||
-                    is_allocated_sectors_min(buf1, n, &n1, min_sparse)) {
-                    ret = blk_write(out_blk, sector_num, buf1, n1);
-                    if (ret < 0) {
-                        error_report("error while writing sector %" PRId64
-                                     ": %s", sector_num, strerror(-ret));
-                        goto out;
-                    }
-                }
-                sector_num += n1;
-                n -= n1;
-                buf1 += n1 * 512;
-            }
-            qemu_progress_print(100.0 * sectors_read / sectors_to_read, 0);
-        }
-    }
 out:
     if (!ret) {
         qemu_progress_print(100, 0);
@@ -1870,7 +1975,6 @@ out:
     qemu_progress_end();
     qemu_opts_del(opts);
     qemu_opts_free(create_opts);
-    qemu_vfree(buf);
     qemu_opts_del(sn_opts);
     blk_unref(out_blk);
     g_free(bs);