diff --git a/fs/operations/multithread.go b/fs/operations/multithread.go
index 6882f23c4..f1e1f18af 100644
--- a/fs/operations/multithread.go
+++ b/fs/operations/multithread.go
@@ -9,6 +9,7 @@ import (
 
 	"github.com/rclone/rclone/fs"
 	"github.com/rclone/rclone/fs/accounting"
+	"github.com/rclone/rclone/lib/multipart"
 	"github.com/rclone/rclone/lib/readers"
 	"golang.org/x/sync/errgroup"
 )
@@ -58,6 +59,7 @@ type multiThreadCopyState struct {
 	acc       *accounting.Account
 	streams   int
 	numChunks int
+	noSeek    bool // set if sure the receiving fs won't seek the input
 }
 
 // Copy a single stream into place
@@ -75,8 +77,9 @@ func (mc *multiThreadCopyState) copyStream(ctx context.Context, stream int, writ
 	if end > mc.size {
 		end = mc.size
 	}
+	size := end - start
 
-	fs.Debugf(mc.src, "multi-thread copy: stream %d/%d (%d-%d) size %v starting", stream+1, mc.numChunks, start, end, fs.SizeSuffix(end-start))
+	fs.Debugf(mc.src, "multi-thread copy: stream %d/%d (%d-%d) size %v starting", stream+1, mc.numChunks, start, end, fs.SizeSuffix(size))
 
 	rc, err := Open(ctx, mc.src, &fs.RangeOption{Start: start, End: end - 1})
 	if err != nil {
@@ -84,12 +87,27 @@ func (mc *multiThreadCopyState) copyStream(ctx context.Context, stream int, writ
 	}
 	defer fs.CheckClose(rc, &err)
 
-	// FIXME NewRepeatableReader is allocating - need to be more careful with the memory allocations
-	// Also allocating for copy to local which doesn't need it
-	bytesWritten, err := writer.WriteChunk(ctx, stream, readers.NewRepeatableReader(rc))
-	if err != nil {
-		return err
+	var rs io.ReadSeeker
+	if mc.noSeek {
+		// Read directly if we are sure we aren't going to seek
+		rs = readers.NoSeeker{Reader: rc}
+	} else {
+		// Read the chunk into buffered reader
+		wr := multipart.NewRW()
+		defer fs.CheckClose(wr, &err)
+		_, err = io.CopyN(wr, rc, size)
+		if err != nil {
+			return fmt.Errorf("multi-thread copy: failed to read chunk: %w", err)
+		}
+		rs = wr
 	}
+
+	// Write the chunk
+	bytesWritten, err := writer.WriteChunk(ctx, stream, rs)
+	if err != nil {
+		return fmt.Errorf("multi-thread copy: failed to write chunk: %w", err)
+	}
+
 	// FIXME: Wrap ReadSeeker for Accounting
 	// However, to ensure reporting is correctly seeks have to be handled properly
 	errAccRead := mc.acc.AccountRead(int(bytesWritten))
@@ -157,6 +175,7 @@ func multiThreadCopy(ctx context.Context, f fs.Fs, remote string, src fs.Object,
 		partSize:  chunkSize,
 		streams:   streams,
 		numChunks: numChunks,
+		noSeek:    f.Features().PartialUploads,
 	}
 
 	// Make accounting