We examine non-minimal supergravity models by omitting some of the usual simplifying assumptions. In particular, the SU(2) × U(1) breaking is uncoupled from the higgsino mass parameter, and the photino to gluino mass ratio is not rigidly fixed. We construct and examine in detail an interesting, and perhaps phenomenologically relevant model, with heavy squarks and light gluinos; the lightest supersymmetric particle is a higgsino h, so the photino decays γ → γh. We discuss ways to determine all of the parameters of the model, and its experimental implications. One interesting consequence is a new way to produce Higgs bosons, e+e− → Z0 → hZ → hhH0, with a rate that depends on the Z mass but could be as large as almost one percent of all Z0 decays even for mH up to about 23of MZ; the signature is H0 + missing energy, which is quite good for detection.