diff --git a/s3/s3.go b/s3/s3.go
index 14542e822..b6cf0aff2 100644
--- a/s3/s3.go
+++ b/s3/s3.go
@@ -150,9 +150,10 @@ func init() {
 
 // Constants
 const (
-	metaMtime     = "Mtime" // the meta key to store mtime in - eg X-Amz-Meta-Mtime
-	listChunkSize = 1024    // number of items to read at once
-	maxRetries    = 10      // number of retries to make of operations
+	metaMtime      = "Mtime"                // the meta key to store mtime in - eg X-Amz-Meta-Mtime
+	listChunkSize  = 1024                   // number of items to read at once
+	maxRetries     = 10                     // number of retries to make of operations
+	maxSizeForCopy = 5 * 1024 * 1024 * 1024 // The maximum size of object we can COPY
 )
 
 // Fs represents a remote s3 server
@@ -751,6 +752,11 @@ func (o *Object) SetModTime(modTime time.Time) error {
 	}
 	o.meta[metaMtime] = aws.String(swift.TimeToFloatString(modTime))
 
+	if o.bytes >= maxSizeForCopy {
+		fs.Debug(o, "SetModTime is unsupported for objects bigger than %v bytes", fs.SizeSuffix(maxSizeForCopy))
+		return nil
+	}
+
 	// Guess the content type
 	contentType := fs.MimeType(o)