diff --git a/backend/s3/s3.go b/backend/s3/s3.go
index c0359029e..473f74ece 100644
--- a/backend/s3/s3.go
+++ b/backend/s3/s3.go
@@ -61,6 +61,7 @@ import (
 	"github.com/rclone/rclone/lib/rest"
 	"github.com/rclone/rclone/lib/version"
 	"golang.org/x/net/http/httpguts"
+	"golang.org/x/sync/errgroup"
 )
 
 // The S3 providers
@@ -2185,10 +2186,10 @@ If empty it will default to the environment variable "AWS_PROFILE" or
 			Sensitive: true,
 		}, {
 			Name: "upload_concurrency",
-			Help: `Concurrency for multipart uploads.
+			Help: `Concurrency for multipart uploads and copies.
 
 This is the number of chunks of the same file that are uploaded
-concurrently.
+concurrently for multipart uploads and copies.
 
 If you are uploading small numbers of large files over high-speed links
 and these uploads do not fully utilize your bandwidth, then increasing
@@ -4507,10 +4508,20 @@ func (f *Fs) copyMultipart(ctx context.Context, copyReq *s3.CopyObjectInput, dst
 
 	fs.Debugf(src, "Starting  multipart copy with %d parts", numParts)
 
-	var parts []*s3.CompletedPart
+	var (
+		parts   = make([]*s3.CompletedPart, numParts)
+		g, gCtx = errgroup.WithContext(ctx)
+	)
+	g.SetLimit(f.opt.UploadConcurrency)
 	for partNum := int64(1); partNum <= numParts; partNum++ {
-		if err := f.pacer.Call(func() (bool, error) {
-			partNum := partNum
+		// Fail fast, in case an errgroup managed function returns an error
+		// gCtx is cancelled. There is no point in uploading all the other parts.
+		if gCtx.Err() != nil {
+			break
+		}
+		partNum := partNum // for closure
+		g.Go(func() error {
+			var uout *s3.UploadPartCopyOutput
 			uploadPartReq := &s3.UploadPartCopyInput{}
 			//structs.SetFrom(uploadPartReq, copyReq)
 			setFrom_s3UploadPartCopyInput_s3CopyObjectInput(uploadPartReq, copyReq)
@@ -4519,18 +4530,24 @@ func (f *Fs) copyMultipart(ctx context.Context, copyReq *s3.CopyObjectInput, dst
 			uploadPartReq.PartNumber = &partNum
 			uploadPartReq.UploadId = uid
 			uploadPartReq.CopySourceRange = aws.String(calculateRange(partSize, partNum-1, numParts, srcSize))
-			uout, err := f.c.UploadPartCopyWithContext(ctx, uploadPartReq)
+			err := f.pacer.Call(func() (bool, error) {
+				uout, err = f.c.UploadPartCopyWithContext(gCtx, uploadPartReq)
+				return f.shouldRetry(gCtx, err)
+			})
 			if err != nil {
-				return f.shouldRetry(ctx, err)
+				return err
 			}
-			parts = append(parts, &s3.CompletedPart{
+			parts[partNum-1] = &s3.CompletedPart{
 				PartNumber: &partNum,
 				ETag:       uout.CopyPartResult.ETag,
-			})
-			return false, nil
-		}); err != nil {
-			return err
-		}
+			}
+			return nil
+		})
+	}
+
+	err = g.Wait()
+	if err != nil {
+		return err
 	}
 
 	return f.pacer.Call(func() (bool, error) {