Improved Naturalness and the Two Higgs Doublet Model
  The natural cutoff scale for the quadratically divergent top quark contribution to the Higgs mass parameter can be significantly raised above the surprisingly low standard model value, with important consequences for the LHC: the physics that cancels the top quark divergence may be out of reach, while an electroweak sector with "improved naturalness" may be discovered. Such a sector, consistent with electroweak precision tests, arises in the two Higgs doublet model with heavy Higgs and top quark interactions that approach strong coupling. 
Riccardo Barbieri and Lawrence J. Hall