The frequency analysis of hydrological extremes requires fitting a probability distribution to the observed data to suitably represent the frequency of occurrence of rare events. The choice of the model to be used for statistical inference is often based on subjective criteria, or it is considered a matter of probabilistic hypotheses testing. In contrast, specific tools for model selection, like the well-known Akaike information criterion (AIC) and the Bayesian information criterion (BIC), are seldom used in hydrological applications. The objective of this study is to verify whether the AIC and BIC work correctly when they are applied to identifying the probability distribution of hydrological extremes, i.e., when the available samples are small and the parent distribution is highly asymmetric. An additional model selection criterion, based on the Anderson-Darling goodness-of-fit test statistic, is here proposed, and the performances of the three methods are compared through an extensive numerical analysis. The capability of the three criteria to recognize the correct parent distribution from the available data samples varies from case to case, and it is rather good in some cases (in particular when the parent is a two-parameter distribution) and unsatisfactory in others. An application to flood peak time series from 1000 catchments located in the United Kingdom provides some further information on the qualities and drawbacks of the considered criteria. From the numerical simulations and data-based analyses it can be concluded that the three model selection techniques considered here produce results of comparable quality.