Many financial markets rely on a discriminatory limit-order book to balance supply and demand. We study these markets in a static model in which uninformed market makers compete in nonlinear tariffs to trade with an informed insider, as in Glosten (1994), Biais, Martimort, and Rochet (2000), and Back and Baruch (2013). We analyze the case where tariffs are unconstrained and the case where tariffs are restricted to be convex. In both cases, we show that pure-strategy equilibrium tariffs must be linear and, moreover, that such equilibria only exist under exceptional circumstances. These results stand in stark contrast with those obtained so far in the literature, reflecting different assumptions about the richness of the insider's information.