The decomposition of unitary representations of a discrete group obtained by induction from a subgroup involves commensurators. In particular Mackey has shown that quasi-regular representations are irreducible if and only if the corresponding subgroups are self-commensurizing. The purpose of this work is to describe general constructions of pairs of groups F 0 < F with F 0 its own commensurator in F. These constructions are then applied to groups of isometries of hyperbolic spaces and to lattices in algebraic groups.