  We explore the effects of a strongly-coupled, approximately scale-invariant
sector on the renormalization of soft supersymmetry breaking terms. A useful
formalism for deriving exact results for renormalization of soft supersymmetry
breaking terms is given in an appendix, and used to generalize previously known
results to include the effects of nontrilinear superpotential terms. We show
that a class of theories which explain the flavor hierarchy without flavor
symmetries can also solve the supersymmetric flavor problem by producing nearly
degenerate masses for the first two generations of scalar superpartners within
each charge sector. Effects from trilinear scalar terms are also suppressed,
although their initial values must be relatively small. Our mechanism results
in testable predictions for the superpartner spectrum.
