This paper presents an equilibrium model of the federal funds market that ties movements in the funds rate to changes in the supply of reserves and to a fixed cost facing banks that borrow at the discount window. It is found that the existence of the fixed cost is capable of explaining a number of features of the funds market. In particular, it is critical for explaining occasional instances of extremely high funds rates. It also provides an explanation for heterogeneous behavior across banks towards the discount window and for higher average funds rates at the end of maintenance periods.