Many conformal field theories are defined by a pair of Lie algebras g ⊃ h. They represent the continuum limit of two-dimensional integrable lattice models. There are a few known examples, such as the three-state Potts model, which are obtained by more than one of these coset constructions. We propose a simple way of systematically building equivalent coset models, and we illustrate it in a lot of cases. We also explain how it can be translated into identities relating the partition functions.