Cooper and Willis (2003) is the latest in a sequence of criticisms of our methodology for estimating aggregate nonlinearities when microeconomic adjustment is lumpy. Their case is based on "reproducing" our main findings using artificial data generated by a model where microeconomic agents face quadratic adjustment costs. That is, they supposedly find our results where they should not be found. The three claims on which they base their case are incorrect. Their mistakes range from misinterpreting their own simulation results to failing to understand the context in which our procedures should be applied. They also claim that our approach assumes that employment decisions depend on the gap between the target and current level of unemployment. This is incorrect as well, since the 'gap approach' has been derived formally from at least as sophisticated microeconomic models as the one they present. On a more positive note, the correct interpretation of Cooper and Willis's results shows that our procedures are surprisingly robust to significant departures from the assumptions made in our original derivations.