Various tasks in decision making and decision support require selecting a preferred subset of items from a given set of feasible items. Recent work in this area considered methods for specifying such preferences based on the attribute values of individual elements within the set. Of these, the approach of (Brafman et al. 2006) appears to be the most general. In this paper, we consider the problem of computing an optimal subset given such a specification. The problem is shown to be NP-hard in the general case, necessitating heuristic search methods. We consider two algorithm classes for this problem: direct set construction, and implicit enumeration as solutions to appropriate CSPs. New algorithms are presented in each class and compared empirically against previous results.