  Models with an extended Higgs sector open up the phenomenological possibility
of additional scalars, beyond the SM-like boson observed by the LHC, with mass
at or below the electroweak scale. Such scenarios are in particular viable in
the presence of electroweak-singlet spin-0 fields, as expected for instance in
the context of the NMSSM. Given that the size of radiative corrections can
substantially affect the Higgs potential, a negative squared mass at the tree
level does not necessarily yield a tachyonic spectrum at the physical level,
but only indicates a failure of the tree-level description for calculational
purposes. We explain how to tackle this technical issue in the example of the
NMSSM, in scenarios with light CP-odd or CP-even singlet-dominated states and
show how loop corrections to the Higgs masses and decay widths can be derived
with the regularized Lagrangian. We further explore how the same flexibility in
the definition of tree-level parameters can be exploited to circumvent large
deviations of the tree-level spectrum from the kinematical setup in Higgs
decays, or to estimate the theoretical uncertainty associated with the
discrepancy between tree-level and physical Higgs spectra. The latter is of
particular relevance for the properties of the SM-like Higgs boson in
supersymmetry-inspired models.
