diff --git a/core/remotes/docker/fetcher.go b/core/remotes/docker/fetcher.go
index 9388d8479e..e32b73b353 100644
--- a/core/remotes/docker/fetcher.go
+++ b/core/remotes/docker/fetcher.go
@@ -442,7 +442,7 @@ func (r dockerFetcher) open(ctx context.Context, req *request, mediatype string,
 
 	chunkSize := int64(r.performances.ConcurrentLayerFetchBuffer)
 	parallelism := int64(r.performances.MaxConcurrentDownloads)
-	if chunkSize < minChunkSize {
+	if chunkSize < minChunkSize || req.body != nil {
 		parallelism = 1
 	}
 	log.G(ctx).WithField("initial_parallelism", r.performances.MaxConcurrentDownloads).
@@ -452,7 +452,9 @@ func (r dockerFetcher) open(ctx context.Context, req *request, mediatype string,
 		Debug("fetching layer")
 	req.setMediaType(mediatype)
 	req.header.Set("Accept-Encoding", "zstd;q=1.0, gzip;q=0.8, deflate;q=0.5")
-	req.setOffset(offset)
+	if parallelism > 1 || offset > 0 {
+		req.setOffset(offset)
+	}
 
 	if err := r.Acquire(ctx, 1); err != nil {
 		return nil, err
@@ -478,7 +480,7 @@ func (r dockerFetcher) open(ctx context.Context, req *request, mediatype string,
 	})
 
 	remaining, _ := strconv.ParseInt(resp.Header.Get("Content-Length"), 10, 0)
-	if parallelism > 1 && req.body == nil {
+	if parallelism > 1 {
 		// If we have a content length, we can use multiple requests to fetch
 		// the content in parallel. This will make download of bigger bodies
 		// faster, at the cost of parallelism more requests and max
diff --git a/core/remotes/docker/fetcher_test.go b/core/remotes/docker/fetcher_test.go
index 104201bf41..262c562d2d 100644
--- a/core/remotes/docker/fetcher_test.go
+++ b/core/remotes/docker/fetcher_test.go
@@ -50,6 +50,10 @@ func TestFetcherOpen(t *testing.T) {
 	s := httptest.NewServer(http.HandlerFunc(func(rw http.ResponseWriter, r *http.Request) {
 		if start > 0 {
 			rw.Header().Set("content-range", fmt.Sprintf("bytes %d-127/128", start))
+		} else if r.Header.Get("Range") == "bytes=0-" {
+			// Simulate registries which do not support range requests
+			rw.WriteHeader(http.StatusBadRequest)
+			return
 		}
 		rw.Header().Set("content-length", strconv.Itoa(len(content[start:])))
 		_, _ = rw.Write(content[start:])