Logistic smooth transition and Markov switching autoregressive models of a logistic transform of the monthly US unemployment rate are estimated by Markov chain Monte Carlo methods. The Markov switching model is identified by constraining the first autoregression coefficient to differ across regimes. The transition variable in the LSTAR model is the lagged seasonal difference of the unemployment rate. Out-of-sample forecasts are obtained from Bayesian predictive densities. Although both models provide very similar descriptions, Bayes factors and predictive efficiency tests (both Bayesian and classical) favor the smooth transition model.