  We study the Dine-Fischler-Srednicki (DFS) model in the light of the recent
Higgs LHC results and electroweak precision data. The DFS model is a natural
extension of the two-Higgs doublet model endowed with a Peccei-Quinn symmetry
and leading to a physically acceptable axion. For generic couplings, the model
reproduces the minimal Standard Model showing only tiny deviations (extreme
decoupling scenario) whereas all additional degrees of freedom (with the
exception of the axion) are very heavy. Recently, new corners of this model
have been highlighted where it may exhibit enlarged global symmetries making
the corresponding models technically natural (naturalness scenario). In some
cases an additional Higgs could be present at the weak scale. In this case, the
new light $0^+$ state would be accompanied by relatively light charged and
neutral pseudoscalar Higgses. We will use the oblique corrections, particularly
$\Delta\rho$, to constrain the mass spectrum in this case. As a final result,
we also work out the non-linear parametrization of the DFS model in the generic
case where all scalars except the lightest Higgs and the axion have masses at
or beyond the TeV scale.
