Multilevel regression with post-stratification (MrP) has quickly become the gold standard for small area estimation. While the first MrP models did not include context-level information, current applications almost always make use of such data. When using MrP, researchers are faced with three problems: how to select features, how to specify the functional form, and how to regularize the model parameters. These problems are especially important with regard to features included at the context level. We propose a systematic approach to estimating MrP models that addresses these issues by employing a number of machine learning techniques. We illustrate our approach based on 89 items from public opinion surveys in the US and demonstrate that our approach outperforms a standard MrP model, in which the choice of context-level variables has been informed by a rich tradition of public opinion research.