We discuss a recently proposed scenario where the sparticle masses are purely mediated by gravity through the superconformal anomaly. This scenario elegantly evades the supersymmetric flavor problem since soft masses, like the anomaly, are not directly sensitive to ultraviolet physics. However, its minimal incarnation fails by predicting tachyonic sleptons. We study the conditions for decoupling of heavy threshold effects and how these conditions are evaded. We use these results to build a realistic class of models where the non-decoupling effects of ultra-heavy vectorlike matter fields eliminate the tachyons. These models have a flavor invariant superspectrum similar to that of gauge mediated models. They, however, differ in several aspects: the gaugino masses are not unified, the colored sparticles are not much heavier than the others, the mu problem is less severe and the gravitino mass is well above the weak scale, m(3/2) greater than or similar to 10 TeV. We also show that in models where an R-symmetry can be gauged, the associated D-term gives rise to soft terms that are similarly insensitive to the ultraviolet.