  We investigate the theoretical stability of the predictions of tri-bimaximal
neutrino mixing with respect to third family wave-function corrections. Such
third family wave-function corrections can arise from either the canonical
normalisation of the kinetic terms or renormalisation group running effects. At
leading order both sorts of corrections can be subsumed into a single universal
parameter. For hierarchical neutrinos, this leads to a new testable lepton
mixing sum rule 's = r cos delta + 2/3 a' (where s, r, a describe the
deviations of solar, reactor and atmospheric mixing angles from their
tri-bimaximal values, and 'delta' is the observable Dirac CP phase) which is
stable under all leading order third family wave-function corrections, as well
as Cabibbo-like charged lepton mixing effects.
