Age-period-cohort models used in life and general insurance can be over-parameterized, and actuaries have used several methods to avoid this, such as cubic splines. Regularization is a statistical approach for avoiding over-parameterization, and it can reduce estimation and predictive variances compared to MLE. In Markov Chain Monte Carlo (MCMC) estimation, regularization is accomplished by the use of mean-zero priors, and the degree of parsimony can be optimized by numerically efficient out-of-sample cross-validation. This provides a consistent framework for comparing a variety of regularized MCMC models, such as those built with cubic splines, linear splines (as ours is), and the limiting case of non-regularized estimation. We apply this to the multiple-trend model of Hunt and Blake (2014).