This paper analyzes the cost of disinflations under real wage rigidities in a micro-founded New Keynesian model. The consensus is that real wage rigidities can be a useful mechanism to induce the inflation persistence that is absent in the standard Calvo model. Real wage rigidities thus generate a slump in output after a credible disinflationary policy. This consensus is flawed, since it depends on analyzing the model in a linearized framework. Once nonlinearities are taken into account, the results change dramatically, both qualitatively and quantitatively. Real wage rigidities imply neither inflation persistence, nor output costs of disinflations. Real wage rigidities actually create a boom after a permanent reduction in the inflation target of the monetary policy.