  Two-Higgs-doublet models (2HDM) are simple extensions of the Standard Model
(SM) where the scalar sector is enlarged by adding a weak doublet. As a result,
the Higgs potential depends in general on several free parameters which have to
be carefully chosen to give predictions consistent with the current precision
data. We consider a 2HDM invariant under a twisted custodial symmetry and
depending only on three extra parameters beyond the SM ones. This model
naturally features an inverted mass spectrum with a light pseudoscalar state
and a heavy SM-like Higgs boson. We thoroughly analyze direct and indirect
constraints and present a few unconventional though promising signatures at the
LHC.
