Lattices have been extensively used for implementing mandatory access control policies. Typically, only a small sublattice of the subset lattice of a certain alphabet is used in applications. We argue that attribute exploration from formal concept analysis is an appropriate tool for generating this sublattice in a semiautomatic fashion. We discuss how two access control models addressing different (in a sense, opposite) requirements can be incorporated within one model. In this regard, we propose two operations that combine contexts of the form (G, M, I) and (N, G, J). The resulting concept lattices provide most of the required structure.