We extend the basic (representative-household) New Keynesian [NK] model of the monetary transmission mechanism to allow for a spread between the interest rate available to savers and borrowers, that can vary for either exogenous or endogenous reasons. We find that the mere existence of a positive average spread makes little quantitative difference for the predicted effects of particular policies. Variation in spreads over time is of greater significance, with consequences both for the equilibrium relation between the policy rate and aggregate expenditure and for the relation between real activity and inflation. Nonetheless, we find that the target criterion - a linear relation that should be maintained between the inflation rate and changes in the output gap - that characterizes optimal policy in the basic NK model continues to provide a good approximation to optimal policy, even in the presence of variations in credit spreads. We also consider a "spread-adjusted Taylor rule," in which the intercept of the Taylor rule is adjusted in proportion to changes in credit spreads. We show that while such an adjustment can improve upon an unadjusted Taylor rule, the optimal degree of adjustment is less than 100 percent; and even with the correct size of adjustment, such a rule of thumb remains inferior to the targeting rule.