Tuned Two-Higgs-Doublet Model

We consider a Two-Higgs-Doublet Model (2HDM) constrained by the condition that assures cancellation of quadratic divergences up to the leading two-loop order. Regions in the parameter space consistent with existing experimental constraints and with the cancellation condition are determined. The possibility for CP violation in the scalar potential is discussed and regions of tan beta - M-H +/- with substantial amount of CP violation are found. The model allows to ameliorate the little hierarchy problem by lifting the minimal scalar Higgs boson mass and by suppressing the quadratic corrections to scalar masses. The cutoff originating from the naturality arguments is therefore lifted from similar to 0.6 TeV in the Standard Model to greater than or similar to 2.5 TeV in the 2HDM, depending on the mass of the lightest scalar.