In supersymmetry, the Higgs quartic couplings is given by the sum in quadra
ture of the weak gauge couplings. This leads to the prediction of a light H
iggs boson, which still holds when considering loop corrections from soft s
upersymmetry breaking. However, another source of corrections, which explic
itly depends on the scale of the mediation of supersymmetry breaking, is fr
om generic hard breaking terms. We show that these corrections can signific
antly modify the Higgs mass prediction in models of low-energy supersymmetr
y breaking, for example, gauge mediation. Conversely, the Higgs mass measur
ement can be used to constrain the scale of mediation of supersymmetry brea
king. (C) 2001 Elsevier Science B.V. All rights reserved.