Abstract: In recent years, many modifications of the Weibull distribution have been proposed. Some of these modifications have a large number of parameters and so their real benefits over simpler modifications are questionable. Here, we use two data sets with modified unimodal (unimodal followed by increasing) hazard function for comparing the exponentiated Weibull and generalized modified Weibull distributions. We find no evidence that the generalized modified Weibull distribution can provide a better fit than the exponentiated Weibull distribution for data sets exhibiting the modified unimodal hazard function.In a related issue, we consider Carrasco et al. (2008), a widely cited paper, proposing the generalized modified Weibull distribution, and illustrating two real data applications. We point out that some of the results in both real data applications in Carrasco et al. (2008) 1 are incorrect.