  Within the MSSM framework and with purely anomaly mediated supersymmetry
breaking the slepton masses turn out to be tachyonic. We resolve this problem
by introducing an anomaly free U(1) gauge symmetry which provides positive
$D$-term contributions to sparticle masses squared that are flavor conserving
at one loop. Two realistic examples based on SU(5) are presented. With U(1)
spontaneously broken at a scale $\sim 10^{16}$ GeV, the right handed neutrinos
acquire masses $\stackrel{<}{_\sim}10^{14}$ GeV. This breaking scale of U(1)
also plays an important role in the proposed resolution of the MSSM $\mu $
problem.
