  Motivated in part by recent demonstrations that electroweak unification into
a simple group may occur at a low scale, we detail the requirements on the
Higgs mass if the unification is to be perturbative. We do this for the
Standard Model effective theory, minimal supersymmetry, and next-to-minimal
supersymmetry with an additional singlet field. Within the Standard Model
framework, we find that perturbative unification with sin2(thetaW)=1/4 occurs
at Lambda=3.8 TeV and requires mh<460 GeV, whereas perturbative unification
with sin2(thetaW)=3/8 requires mh<200 GeV. In supersymmetry, the presentation
of the Higgs mass predictions can be significantly simplified, yet remain
meaningful, by using a single supersymmetry breaking parameter Delta_S. We
present Higgs mass limits in terms of Delta_S for the minimal supersymmetric
model and the next-to-minimal supersymmetric model. We show that in
next-to-minimal supersymmetry, the Higgs mass upper limit can be as large as
500 GeV even for moderate supersymmetry masses if the perturbative unification
scale is low (e.g., Lambda=10 TeV).
