  We introduce a strategy to study the parameter space of the general,
CP-conserving, two-Higgs-doublet Model (2HDM) with a softly broken Z_2-symmetry
by means of a new "hybrid" basis. In this basis the input parameters are the
measured values of the mass of the observed Standard Model (SM)-like Higgs
boson and its coupling strength to vector boson pairs, the mass of the second
CP-even Higgs boson, the ratio of neutral Higgs vacuum expectation values, and
three additional dimensionless parameters. Using the hybrid basis, we present
numerical scans of the 2HDM parameter space where we survey available parameter
regions and analyze model constraints. From these results, we define a number
of benchmark scenarios that capture different aspects of non-standard Higgs
phenomenology that are of interest for future LHC Higgs searches.
