  The sign of the supersymmetric Higgs mass \mu is usually taken as an
independent input parameter in analyses of the supersymmetric standard model. I
study the role of theories of supersymmetry breaking in determining the sign of
\mu as an output. Models with vanishing soft scalar couplings at the apparent
gauge coupling unification scale are known to predict positive \mu. I
investigate more general results for the sign of \mu as a function of the
holomorphic soft scalar couplings, and compare to predictions of models with
gaugino mass dominance at higher scales. In a significant region of the
B_0/m_{1/2} versus A_0/m_{1/2} plane including A_0 = B_0 = 0, \mu must be
positive. In another region, \mu is definitely negative. Only in a smaller
intermediate region does knowledge of the supersymmetry breaking mechanism not
permit a definite prediction of the sign of \mu. The last region will shrink
considerably as the top quark mass becomes more accurately known.
