Faceted Search is a widely used interaction scheme in digital libraries, e-commerce, and recently also in Linked Data. Surprisingly, object ranking in the context of Faceted Search is not well studied in the literature. In this article, we propose an extension of the model with two parameters that enable specifying the desired answer size and the granularity of the sought object ranking. These parameters allow tackling the problem of too big or too small answers and can specify how refined the sought ranking should be. Then, we provide an algorithm that takes as input these parameters and by considering the hard-constraints (filters), the soft-constraints (preferences), as well as the statistical properties of the dataset (through various frequency-based ranking schemes), produces an object ranking that satisfies these parameters, in a transparent way for the user. Then, we present extensive simulation-based evaluation results that provide evidence that the proposed model also improves the answers and reduces the user’s cost. Finally, we propose GUI extensions that are required and present an implementation of the model.