The authors examine the implications for the optimal interest rate rule that follow from relaxing the assumption that the policy-maker's loss function is quadratic. They investigate deviations from quadratics for both symmetric and asymmetric preferences for a single target and find that (i) other characterisations of risk aversion than implied by the quadratic only affect dead-weight losses, unless there is multiplicative uncertainty; and (ii) asymmetries affect the optimal rule under both additive and multiplicative uncertainty but result in interest rate paths observationally similar, and in some cases equivalent, to those implied by a shifted quadratic. The results suggest that in the context of monetary policy-making the convenient assumption of quadratic losses may not be that drastic after all.