We apply a specialized Bayesian method that helps us deal with the methodological challenge of unobserved heterogeneity among immigrant voters. Our approach is based on generalized linear mixed Dirichlet models (GLMDMs) where random effects are specified semiparametrically using a Dirichlet process mixture prior that has been shown to account for unobserved grouping in the data. Such models are drawn from Bayesian nonparametrics to help overcome objections handling latent effects with strongly informed prior distributions. Using 2009 German voting data of immigrants, we show that for difficult problems of missing key covariates and unexplained heterogeneity this approach provides (1) overall improved model fit, (2) smaller standard errors on average, and (3) less bias from omitted variables. As a result, the GLMDM changed our substantive understanding of the factors affecting immigrants' turnout and vote choice. Once we account for unobserved heterogeneity among immigrant voters, whether a voter belongs to the first immigrant generation or not is much less important than the extant literature suggests. When looking at vote choice, we also found that an immigrant's degree of structural integration does not affect the vote in favor of the CDU/CSU, a party that is traditionally associated with restrictive immigration policy.