Traditional methods (linear regression, spline fitting) of age-depth modeling generate overly optimistic confidence intervals. Originally developed for C, Bayesian models (use of observations independent of chronology) allow the incorporation of prior information about superposition of dated horizons, stratigraphic position of undated points, and variations in sedimentology and sedimentation rate into model fitting. We modified the methodology of two Bayesian age depth models, Bchron (Haslett and Parnell, 2008) and OxCal (Ramsey, 2008) for use with U-Pb dates. Some practical implications of this approach include: a) model age uncertainties increase in intervals that lack closely spaced age constraints; b) models do not assume normal distributions, allowing for the non-symmetric uncertainties of sometimes complex crystal age probability functions in volcanic tuffs; c) superpositional constraints can objectively reject some cases of zircon inheritance and mitigate apparent age complexities. We use this model to produce an age-depth model with continuous and realistic uncertainties, for the early Miocene Santa Cruz Formation (SCF), Argentina.