Empirical researchers studying party systems often struggle with the question of how to count parties. Indexes of party system fragmentation used to address this problem (e.g., the effective number of parties) have a fundamental shortcoming: since the same index value may represent very different party systems, they are impossible to interpret and may lead to erroneous inference. We offer a novel approach to this problem: instead of focusing on index measures, we develop a model that predicts the entire distribution of party vote-shares and, thus, does not require any index measure. First, a model of party counts predicts the number of parties. Second, a set of multivariate t models predicts party vote-shares. Compared to the standard index-based approach, our approach helps to avoid inferential errors and, in addition, yields a much richer set of insights into the variation of party systems. For illustration, we apply the model on two data sets. Our analyses call into question the conclusions one would arrive at by the index-based approach. Software is provided to implement the proposed model.