  We determine the allowed parameter space of the CP-conserving
two-Higgs-doublet model (2HDM) of type II with a softly broken Z_2 symmetry.
Our analysis includes theoretical constraints from vacuum stability and
perturbativity as well as experimental constraints from signal strengths of the
126 GeV Higgs boson, the non-observation of additional Higgs resonances and
electroweak precision and flavour observables. If the 126 GeV resonance is
interpreted as the light CP-even Higgs boson of the 2HDM our analysis shows
that scenarios where the couplings of this boson deviate substantially from
those of the SM Higgs boson are disfavoured at one standard deviation and
completely excluded for small values of tan(beta). We also discuss bounds on
the masses of the heavy 2HDM Higgs bosons and their implications for the
possible decay modes of these particles. We find that the region in which both
non-standard neutral Higgs bosons are simultaneously lighter than 300 GeV is
excluded at two standard deviations.
