  We discuss local supercurrents as sources of the super-Einstein equations in
the superconformal approach in the old and new minimal (auxiliary fields)
formulation. Modifications of the Ward identity giving the covariant divergence
of the Einstein multiplet are considered in presence of a Fayet-Iliopoulos
term. Curvature multiplets can be used as alternative to the gravitino
variation in the search for rigid supersymmetric curved backgrounds.
