Databases of 3D shapes have become widespread for a variety of applications, and a key research problem is searching these databases for similar shapes. This paper introduces a method for finding distinctive features of a shape that are useful for determining shape similarity. Although global shape descriptors have been developed to facilitate retrieval, they fail when local shape properties are the distinctive features of a class. Alternatively, local shape descriptors can be generated over the surface of shapes, but then storage and search of the descriptors becomes unnecessarily expensive, as perhaps only a few descriptors are sufficient to distinguish classes. The challenge is to select local descriptors from a query shape that are most distinctive for retrieval. Our approach is to define distinction as the retrieval performance of a local shape descriptor. During a training phase, we estimate descriptor likelihood using a multi-variate Gaussian distribution of real-valued shape descriptors, evaluate the retrieval performance of each descriptor from a training set, and average these performance values at every likelihood value. For each query, we evaluate the likelihood of local shape descriptors on its surface and lookup the expected retrieval values learned from the training set to determine their predicted distinction values. We show that querying with the most distinctive shape descriptors provides favorable retrieval performance during tests with a database of common graphics objects.