  We prove that the family of measured dynamical systems which can be realised
as uniquely ergodic minimal homeomorphisms on a given manifold (of dimension at
least two) is stable under measured extension. As a corollary, any ergodic
system with an irrational eigenvalue is isomorphic to a uniquely ergodic
minimal homeomorphism on the two-torus. The proof uses the following
improvement of Weiss relative version of Jewett-Krieger theorem: any extension
between two ergodic systems is isomorphic to a skew-product on Cantor sets.
