  We point out a synergy between T-conjugated oscillation channels in the
determination of the neutrino mass hierarchy with oscillation experiments with
relatively short baselines (L < 700 km), where the matter effect is small. If
information from all four oscillation channels $\nu_\mu\to\nu_e$,
$\bar\nu_\mu\to\bar\nu_e$, $\nu_e\to\nu_\mu$ and $\bar\nu_e\to\bar\nu_\mu$ is
available, a matter effect of few percent suffices to break the sign-degeneracy
and allows to determine the neutrino mass hierarchy. The effect is discussed by
analytical considerations of the relevant oscillation probabilities, and
illustrated with numerical simulations of realistic experimental setups.
Possible configurations where this method could be applied are the combination
of a super beam experiment with a beta beam or a neutrino factory, or a (low
energy) neutrino factory using a detector with muon and electron charge
identification.
