diff --git a/fs/operations/multithread.go b/fs/operations/multithread.go
index 9abd5f743..c106a4565 100644
--- a/fs/operations/multithread.go
+++ b/fs/operations/multithread.go
@@ -64,25 +64,15 @@ type multiThreadCopyState struct {
 }
 
 // Copy a single chunk into place
-func (mc *multiThreadCopyState) copyChunk(ctx context.Context, chunk int, writer fs.ChunkWriter) (err error) {
+func (mc *multiThreadCopyState) copyChunk(ctx context.Context, chunk int, writer fs.ChunkWriter, start, end, size int64, rw *pool.RW) (err error) {
 	defer func() {
+		if !mc.noBuffering {
+			fs.CheckClose(rw, &err)
+		}
 		if err != nil {
 			fs.Debugf(mc.src, "multi-thread copy: chunk %d/%d failed: %v", chunk+1, mc.numChunks, err)
 		}
 	}()
-	start := int64(chunk) * mc.partSize
-	if start >= mc.size {
-		return nil
-	}
-	end := min(start+mc.partSize, mc.size)
-	size := end - start
-
-	// Reserve the memory first so we don't open the source and wait for memory buffers for ages
-	var rw *pool.RW
-	if !mc.noBuffering {
-		rw = multipart.NewRW().Reserve(size)
-		defer fs.CheckClose(rw, &err)
-	}
 
 	fs.Debugf(mc.src, "multi-thread copy: chunk %d/%d (%d-%d) size %v starting", chunk+1, mc.numChunks, start, end, fs.SizeSuffix(size))
 
@@ -226,9 +216,24 @@ func multiThreadCopy(ctx context.Context, f fs.Fs, remote string, src fs.Object,
 		if gCtx.Err() != nil {
 			break
 		}
-		chunk := chunk
+
+		// Work out how big and where the chunk is
+		start := int64(chunk) * mc.partSize
+		if start >= mc.size {
+			continue
+		}
+		end := min(start+mc.partSize, mc.size)
+		size := end - start
+
+		// Reserve the memory first so we don't open the source and wait for memory buffers for ages
+		// This also avoids creating an excess of goroutines all waiting on memory.
+		var rw *pool.RW
+		if !mc.noBuffering {
+			rw = multipart.NewRW().Reserve(size)
+		}
+
 		g.Go(func() error {
-			return mc.copyChunk(gCtx, chunk, chunkWriter)
+			return mc.copyChunk(gCtx, chunk, chunkWriter, start, end, size, rw)
 		})
 	}