Parties often are associated with specific issues. They can “own” an issue when they develop a reputation of competence and attention in that domain. While there is much aggregate-level evidence on the relation between issue salience and party results, the individual-level mechanisms are less well understood. This paper develops an individual-level model of issue ownership effects. It suggests distinguishing between two aspects of issue ownership: the degree to which voters consider parties to be competent for solving a given issue, and the level of their perceived engagement on that issue. Furthermore, the model suggests that the effects of both aspects of ownership (i.e., competence and engagement) are party-specific. When a party owns an issue, voters’ preferences on the corresponding issue have a larger impact on the evaluation of the issue owner. But this will not necessarily affect the criteria by which other parties are evaluated. These hypotheses are tested with a statistical model that allows the impact of voter-party issue distances on party utilities to vary across both parties and issues, as a function of parties’ perceived engagement and competence. This model is applied to data from the 2011 Swiss election study.