We model the behavior of Nasdaq momentum traders, also known as SOES bandits. We show, all things being equal, that the profitability of SOES bandits decreases in the bid-ask spread, but increases in the effective tick size. The patterns we observe in the data provide support for the model. We then discuss the plausibility of odd-eighth tick avoidance by market makers as a defense against SOES bandits. (Journal of Financial Economics)