A Bayesian approach to estimation, prediction and model comparison in composed error production models is presented. A broad range of distributions on the inefficiency term define the contending models, which can either be treated separately or pooled. Posterior results are derived for the individual efficiencies as well as for the parameters, and the differences with the usual sampling-theory approach are highlighted. The required numerical integrations are handled by Monte Carlo methods with Importance Sampling, and an empirical example illustrates the procedures.