  We show that the simplest supersymmetric scenario where a large Higgs mass
can be attained at tree-level for any ratio of the Higgs vacuum expectation
values corresponds to the case where the neutrino masses are generated through
the type II seesaw mechanism. This allows a standard model-like Higgs with mass
around 125 GeV without assuming a heavy spectrum for the stops. We show that
our results are consistent with the bounds coming from perturbativity up to the
grand unified scale, discuss gauge coupling unification and possible signals at
the Large Hadron Collider.
