  A low-energy non-unitary leptonic mixing matrix is a generic effect of a
large class of theories accounting for neutrino masses. It is shown how the
extra CP-odd phases of a general non-unitary matrix allow for sizeable
CP-asymmetries in channels other than those dominant in the standard unitary
case. The $\nu_\mu\to \nu_\tau$ channel turns out to be an excellent tool to
further constrain moduli and phases. Furthermore, we clarify the relationship
between our approach and the so-called "non-standard neutrino interactions"
schemes: the sensitivities explored here apply as well to such constructions.
