ABSTRACT: We analyze the following method for shuffling $n$ cards. First, remove card 1 (i.e., the card with label 1) and then re-insert it randomly into the deck. Then repeat with cards 2, 3,..., $n$. Call this a round. R. Pinsky showed, somewhat surprisingly, that the mixing time is greater than one round. We show that in fact the mixing time is on the order of $\log n$ rounds. Joint work...