  In supersymmetric models extended with a gauge singlet the mass of the
lightest Higgs boson has contributions proportional to the adimensional
coupling $\lambda$. In minimal scenarios, the requirement that this coupling
remains perturbative up to the unification scale constrains $\lambda$ to be
smaller than $\approx 0.7$. We study the maximum value of $\lambda$ consistent
with a perturbative unification of the gauge couplings in models containing
nonstandard fields at intermediate scales. These fields appear in scenarios
with gauge mediation of supersymmetry breaking. We find that the presence of
extra fields can raise the maximum value of $\lambda$ up to a 19%, increasing
the limits on the mass of the lightest Higgs from 135 GeV to 155 GeV.
