  The effects of supersymmetry breaking are usually parameterized by soft
couplings of positive mass dimensions. However, realistic models also predict
the existence of suppressed, but non-vanishing, dimensionless
supersymmetry-breaking couplings. These couplings are technically hard, but do
not lead to disastrous quadratic divergences in scalar masses, and may be
crucial for understanding low-energy physics. In particular, analytic scalar
quartic couplings that break supersymmetry can lead to intermediate scale
vacuum expectation values along nearly-flat directions. I study the one-loop
effective potential for flat directions in the presence of dimensionless
supersymmetry-breaking terms, and discuss the corresponding renormalization
group equations. I discuss two applications: a minimal model of automatic
R-parity conservation, and an extension of this minimal model which provides a
solution to the \mu problem and an invisible axion.
