If it's kept dry, it falls off faster – usually within two weeks. Besides, newborns don't get very dirty! If the umbilical cord does get wet, pat it dry. And if the stump bleeds a little when the cord falls off, that's okay, too, as Alyson Bracken, of West Roxbury, Massachusetts, learned. "It scared me at first," she says, but then she found out that, as with a scab, mild bleeding was normal.