  Non-Standard neutrino Interactions (NSI) are vector contact interactions
involving two neutrinos and two first generation fermions, which can affect
neutrino propagation in matter. SU(2) gauge invariance suggests that NSI should
be accompanied by more observable charged lepton contact interactions. However,
these can be avoided at tree level in various ways. We focus on lepton
flavour-changing NSI, suppose they are generated by New Physics heavier than
$m_W$ that does not induce (charged) Lepton Flavour Violation (LFV) at tree
level, and show that LFV is generated at one loop in most cases. The current
constraints on charged Lepton Flavour Violation therefore suggest that mu <--->
e flavour-changing NSI are unobservable and tau <---> l flavour-changing NSI
are an order of magnitude weaker than the weak interactions. This conclusion
can be avoided if the heavy New Physics conspires to cancel the one-loop LFV,
or if NSI are generated by light New Physics to which our analysis does not
apply.
