The increasing popularity of the Spatial Theory of Voting has given rise to the frequent usage of multinomial logit/probit models with alternative-specific covariates. The flexibility of these models comes along with one severe drawback: the proliferation of coefficients, resulting in high-dimensional and difficult-to-interpret models. In particular, choice models in a party system with J parties result in maximally J − 1 parameters for chooser-specific attributes (e.g., sex, age). For the specification of alternative-specific attributes (e.g., issue distances), maximally J parameters can be estimated. Thus, a model of party choice with five parties based on three issues and ten voter attributes already produces 59 possible coefficients.As soon as we allow for interaction effects to detect segment-specific reactions to issues, the situation is even aggravated. In order to systematically identify relevant predictors in spatial voting models, we derive and use for the first time Lasso-type regularized parameter selection techniques that take into account both individualand alternative-specific variables. Most importantly, our new algorithm can handle the alternative-wise specification of issue distances. Applying the Lasso method to the 2009 German Parliamentary Election, we demonstrate that our approach massively reduces the model's complexity and simplifies its interpretation. Lassopenalization clearly outperforms the simple ML estimator.