Signicant progress has been made towards the generalization of somewellknown lifetime models, which have been successfully applied toproblems arising in several areas of research. In this paper, some prop-erties of the new Kumaraswamy exponential-Weibull (KwEW) distribu-tion are provided. This distribution generalizes a number of well-knownspecial lifetime models such as the Weibull, exponential, Rayleigh, mod-ied Rayleigh, modied exponential and exponentiated Weibull dis-tributions, among others. The beauty and importance of the newdistribution lies in its ability to model monotone and non-monotonefailure rate functions, which are quite common in environmental stud-ies. We derive some basic properties of the KwEW distribution in-cluding ordinary and incomplete moments, skewness, kurtosis, quantileand generating functions, mean deviations and Shannon entropy. Themethod of maximum likelihood and a Bayesian procedure are used forestimating the model parameters. By means of a real lifetime dataset, we prove that the new distribution provides a better t than theKumaraswamy Weibull, Marshall-Olkin exponential-Weibull, extendedWeibull, exponential-Weibull and Weibull models. The application in-dicates that the proposed model can give better ts than other well-known lifetime distributions.