We present a novel angle for multi-armed bandits (henceforth abbreviated MAB) which follows from the recent work on MAB mechanisms (Devanur and Kakade, 2009, Babaio et al., 2009, 2010). The new problem is, essentially, about designing MAB algorithms under an additional constraint motivated by their application to MAB mechanisms. This note is self-contained, although some familiarity with MAB is assumed; we refer the reader to Cesa-Bianchi and Lugosi (2006) for more background.