This paper describes a semiparametric Bayesian method for analyzing duration data. The proposed estimator specifies a complete functional form for duration spells, but allows flexibility by introducing an individual heterogeneity term, which follows a Dirichlet mixture distribution. I show how to obtain predictive distributions for duration data that correctly account for the uncertainty present in the model. I also directly compare the performance of the proposed estimator with Heckman and Singer's (1984) Non Parametric Maximum Likelihood Estimator (NPMLE). The methodology is applied to the analysis of youth unemployment spells. Compared to the NPMLE, the proposed estimator reflects more accurately the uncertainty surrounding the heterogeneity distribution.