We explore, in the MSSM context, an extension of the Anomaly Mediated Super
symmetry Breaking solution for the soft scalar masses that is possible if t
he underlying theory has a gauged R-symmetry. The slepton mass problem char
acteristic of the scenario is resolved, and a context for the explanation o
f the fermion mass hierarchy provided. (C) 2000 Published by Elsevier Scien
ce B.V.