Fayet-Iliopoulos D-terms and anomaly mediated supersymmetry breaking

We show that in a minimal extension of the MSSM by means of an extra U(1) gauge group, the negative mass-squared problem characteristic of the Anomaly Mediated Supersymmetry Breaking scenario is naturally solved by means of Fayet-Iliopoulos D-terms. We derive a set of sum rules for the sparticle masses which are consequences of the resulting framework.