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The model choice problem in Hydrology is illustrated by means of the optimum levee design for flat rivers along a confluence reach. Special attention is given to the selection of a probability distribution for the joint flood stages. The optimality criterion used is the minimization of construction plus expected flood damage costs. The main assumption in the mathematical model is that the levee profile is uniquely determined as a function of the levee heights at the extremes of the reach; thus the problem is reduced to the determination of the optimum pair of extreme levee heights. The selection of a probability distribution of flood stages, from a set of distributions estimated from the partial duration series, is performed using either one of two selection procedures: likelihood of the Chi -square statistic and sample likelihoods. A composite distribution, taking into account the model uncertainty, is also derived. The methodology presented is applied to the remodeling of the levee on the west bank of the Zagyva River, in Hungary. A sensitivity analysis is performed, using the best ranking distributions according to the two model choice procedures. The composite distribution appears to offer a reasonable choice.