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When a market order arrives, the NYSE specialist can offer a price one tick better than the limit orders on the book and trade for his own account. Alternatively, the specialist can "stop" the market order, which means he guarantees execution at the current quote but provides the possibility of price improvement. My model shows that specialists can use stops to sample the future order flow before making a commitment to trade. I present empirical evidence that both stops and immediate price improvement impose adverse selection costs on limit order traders. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.