  The upper limit on the mass of the lightest CP-even neutral Higgs in the
minimal supersymmetric standard model is around 135 GeV for soft supersymmetry
breaking masses in the 1 TeV range. We demonstrate that this upper limit may be
sizably relaxed if supersymmetry is embedded in extra dimensions. We calculate,
using the effective potential technique, the radiative corrections to the
lightest Higgs mass induced by the Kaluza-Klein towers of quarks and squarks
with one and two compactified directions. We observe that the lightest Higgs
may comfortably weigh around 200 GeV (300 GeV) with one (two) extra
dimension(s).
