diff --git a/fs/operations/multithread.go b/fs/operations/multithread.go
index b8ace21d5..62812dc00 100644
--- a/fs/operations/multithread.go
+++ b/fs/operations/multithread.go
@@ -28,11 +28,15 @@ func doMultiThreadCopy(ctx context.Context, f fs.Fs, src fs.Object) bool {
 	if ci.MultiThreadStreams <= 1 {
 		return false
 	}
+	// ...if the source doesn't support it
+	if src.Fs().Features().NoMultiThreading {
+		return false
+	}
 	// ...size of object is less than cutoff
 	if src.Size() < int64(ci.MultiThreadCutoff) {
 		return false
 	}
-	// ...source doesn't support it
+	// ...destination doesn't support it
 	dstFeatures := f.Features()
 	if dstFeatures.OpenWriterAt == nil {
 		return false
diff --git a/fs/operations/multithread_test.go b/fs/operations/multithread_test.go
index fa982cf59..aef6f75af 100644
--- a/fs/operations/multithread_test.go
+++ b/fs/operations/multithread_test.go
@@ -79,6 +79,11 @@ func TestDoMultiThreadCopy(t *testing.T) {
 	assert.True(t, doMultiThreadCopy(ctx, f, src))
 	srcFs.Features().IsLocal = false
 	assert.True(t, doMultiThreadCopy(ctx, f, src))
+
+	srcFs.Features().NoMultiThreading = true
+	assert.False(t, doMultiThreadCopy(ctx, f, src))
+	srcFs.Features().NoMultiThreading = false
+	assert.True(t, doMultiThreadCopy(ctx, f, src))
 }
 
 func TestMultithreadCalculateChunks(t *testing.T) {