In [23], Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve Rees construction, allowing to start with any homeomorphism R instead of an irrational rotation and to control precisely the measurable dynamics of f . This yields in particular the following result: Any compact manifold of dimension d ≥ 2 which carries a minimal uniquely ergodic homeomorphism also carries a minimal uniquely ergodic homeomorphism with positive topological entropy.More generally, given some homeomorphism R of a (compact) manifold and some homeomorphism h C of a Cantor set, we construct a homeomorphism f which "looks like" R from the topological viewpoint and "looks like" R × h C from the measurable viewpoint. This construction can be seen as a partial answer to the following realisability question: which measurable dynamical systems are represented by homeomorphisms on manifolds ?AMS classification. 37E30, 37B05, 37B40.