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We study the effects of disorder on the slope of the disorder--temperaturephase boundary near the Onsager point (Tc = 2.269...) in spin-glass models. Sofar, studies have focused on marginal or irrelevant cases of disorder. Usingduality arguments, as well as exact Pfaffian techniques we reproduce theseanalytical estimates. In addition, we obtain different estimates for spin-glassmodels on hierarchical lattices where the effects of disorder are relevant. Weshow that the phase-boundary slope near the Onsager point can be used to probefor the relevance of disorder effects.

Universality in phase boundary slopes for spin glasses on self dual lattices