--- src/copy.c
+++ src/copy.c
@@ -1044,6 +1044,8 @@ copy_reg (char const *src_name, char const *dst_name,
           buf_size -= buf_size % blcm;
           if (buf_size == 0 || blcm_max < buf_size)
             buf_size = blcm;
+
+          fallocate(dest_desc, FALLOC_FL_KEEP_SIZE, 0, src_sb->st_size);
         }
 
       /* Make a buffer with space for a sentinel at the end.  */