We suggest and analyze a class of supersymmetric Z' models based on the gauge symmetry U(1)_x = x Y - (B-L), where Y is the Standard Model hypercharge. For 1 < x < 2, the U(1)_x D-term generates positive contributions to the slepton masses, which is shown to solve the tachyonic slepton problem of anomaly mediated supersymmetry breaking (AMSB). The resulting models are very predictive, both in the SUSY breaking sector and in the Z' sector. We find M_Z' = (2-4) TeV and the Z-Z' mixing angle ξ= 0.001. Consistency with symmetry breaking and AMSB phenomenology renders the Z' "leptophobic", with Br(Z' -> e^+ e^-) = (1-1.6)% and Br(Z' -> q q-bar) = 44%. The lightest SUSY particle is either the neutral Wino or the sneutrino in these models.

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