Three detailed case studies illustrating the seasonal analysis of economic time series are presented using component models for seasonal and nonseasonal behavior. Analyses are performed within a semi-Bayesian framework where inferences for target quantities of interest, such as seasonally adjusted values, are obtained as posterior distributions conditional on observed data and fitted parameter values. Such an approach is similar to previous model-based methods of seasonal analysis, but new models and algorithms are used and, more important, a sensitivity analysis is performed to determine the extent to which conclusions vary across a range of plausible fitted models. It is found that sensitivity to variation across plausible models is not unusual in practice. The logical conclusion of the investigation is that a fully Bayesian analysis is required that averages conditional posteriors over a posterior distribution for the model parameters. Such an analysis is necessarily sensitive to the choice of prior distribution. We believe that such dependencies on assumptions external to the data are inevitable in complex problems such as seasonal adjustment. The stochastic components of our nonseasonal and seasonal models are based on modified fractional Gaussian noise, as described in Carlin, Dempster, and Jonas (1985). The models allow for joint estimation of both fixed and random effects, a capability that is used to estimate the initial values of nonstationary components and is further illustrated in the data analysis by the use of trading-day adjustments. Our model structure is described in detail, but technical details of algorithms used to perform likelihood and conditional posterior calculations for fitted models are omitted in favor of the empirical case studies. The examples include some comparisons to the nonparametric X-11 method and to an autoregressive moving average modeling approach. One of the examples exhibits particularly striking differences between the model-based seasonal adjustments and those of X-11.