  The effects of heavy mass thresholds on anomaly-mediated soft supersymmetry
breaking terms are discussed. While heavy thresholds completely decouple to
lowest order in the supersymmetry breaking, it is argued that they do affect
the breaking terms at higher orders. The relevant contributions typically occur
at lower order in the loop expansion compared to purely anomaly mediated
contributions. The non decoupling contributions may be used to render models in
which the only source of supersymmetry breaking is anomaly mediation viable, by
generating positive contributions to the sleptons' masses squared. They can
also be used to generate acceptable mu- and B-terms.
