We construct a model to analyse the two types of tender procedures used by the European Central Bank in its open market operations. We assume that the ECB minimizes the expected value of a loss function that depends on the quadratic difference between the interbank rate and a target interest rate that characterizes the stance of monetary policy. We show that when the loss function penalizes more heavily interbank rates below the target, fixed rate tenders have a unique equilibrium characterized by extreme overbidding. We also show that variable rate tenders have multiple equilibria characterized by varying degrees of overbidding, and that in these tenders an equilibrium without overbidding can be obtained by preannoucing the intended liquidity injection. Finally, our empirical analysis supports the assumption of an asymmetric loss function for the ECB.