  We consider an expression for the supercurrent in the superconformal
formulation of N=1 supergravity. A chiral compensator provides the
supersymmetric formulation of the Callan-Coleman-Jackiw (CCJ) improved stress
energy tensor, when the conformal gauge is used. Superconformal and
non-superconformal matter give different conservation laws of the supercurrent,
when coupled to the curvature supermultiplets which underlie the local
superspace geometry. This approach can be applied to any set of auxiliary
fields and it is useful to classify rigid curved superspace geometries.
Examples with four supersymmetries are briefly described.
