Recent research has highlighted the benefits of completeness as a retrieval criterion in recommender systems. In complete retrieval, any subset of the constraints in a given query that can be satisfied must be satisfied by at least one of the retrieved products. Minimal completeness (i.e., always retrieving the smallest set of products needed for completeness) is also beginning to attract research interest as a way to minimize cognitive load in the approach. Other important features of a retrieval algorithm’s behavior include the diversity of the retrieved products and the order in which they are presented to the user. In this paper, we present a new algorithm for minimally complete retrieval (MCR) in which the ranking of retrieved products is primarily based on the number of constraints that they satisfy, but other measures such as similarity or utility can also be used to inform the retrieval process. We also present theoretical and empirical results that demonstrate our algorithm’s ability to minimize cognitive load while ensuring the completeness and diversity of the retrieved products.