Exact results for the soft supersymmetry breaking b-functions
are reviewed, and used to derive ('bottom-up') the superconformal
anomaly-inspired results for the soft parameters, and a distinct
RG-invariant solution for the finite case.
Classes of soft masses and interactions that are not usually
considered, both in general and in the MSSM context are explored.
Preliminary results for the effect on the sparticle spectrum of such
theories are presented. A new class of (at least) one-loop finite
theories is constructed. The infra-red stability of fixed points in the
evolution of the Yukawa couplings, A-parameters and soft masses
is investigated. In a wide range of physically interesting theories it
is shown that, in the asymptotically free case, the existence of
stable IR fixed points for the Yukawa couplings implies stable IR
fixed points for the A parameters and soft masses.
