  We obtain a {\it complete set} of one-loop RGE's for a set of combinations of
neutrino parameters for the case of two-fold degenerate hierarchical
three-neutrino models. The requirement of consistency of exact solutions to
these RGE's with the two-fold degeneracy yields conditions which have
previously been obtained perturbatively/numerically. These conditions, in the
limit $|U_{e\nu_{3}}|=0$, are shown to lead to a strong cancellation in the
matrix element of neutrinoless double beta decay.
