We investigate the implications of rule-of-thumb behaviour on the part of consumers or price setters for optimal monetary policy and simple interest rate rules. The existence of such behaviour leads to endogenous persistence in output and inflation; changes the transmission of shocks to these variables; and alters the policymaker's welfare objective. Our main finding is that highly inertial policy is optimal regardless of what fraction of agents occasionally follow a rule of thumb. We also find that the interest rate rule that implements optimal policy in the purely optimising case, and a first-difference version of Taylor's (1993) rule, have desirable properties in all of the cases we consider. By contrast, the coefficients in other optimised simple rules tend to be extremely sensitive with respect to the fraction of rule-of-thumb behaviour and changes in other parameters of the model.