We introduce the extended perturbation method, which improves the accuracy of standard perturbation by reducing approximation errors under certainty equivalence. For the New Keynesian model with Calvo pricing, extended perturbation is more accurate than standard perturbation, which implies explosive dynamics because it omits the upper bound on inflation implied by this model. In contrast, extended perturbation enforces this bound and generates stable dynamics. We also show that extended perturbation can accurately solve a New Keynesian model that enforces the zero lower bound for the monetary policy rate by considering a smooth nonlinear modification of the standard Taylor rule.