In this paper we propose a novel minimality criterion for models of modal logics based on a variation of the notion of simulation, called subset-simulation. We present a minimal model sound and complete tableau calculus for the generation of this new kind of minimal models for the multi-modal logic K (m), and we discuss extensions to cover more expressive logics. The generation of minimal models is performed incrementally by using a minimality test to close branches representing non-minimal models, or to update the set of minimal models. Subset-simulation minimal models have the advantage that they are semantically more natural than models obtained by using syntactic minimality criteria.