  We revisit the supermultiplet structure of Noether currents for N=1
supersymmetric gauge theories. Using superfield identities and the field
equations we show how to derive a superfield equation for the divergences of
the Noether currents in terms of the supercurrent and anomaly superfields
containing 16_B+16_F components. We refer to this as the natural supercurrent
structure as it is invariant under all local symmetries of the theory. It
corresponds to the S-multiplet of Komargodski and Seiberg. We clarify the
on/off-shell nature of the currents appearing in this multiplet and we study in
detail the effect of specific improvement transformations leading to 1) a
Ferrara-Zumino multiplet and to 2) a multiplet containing the new improved
energy-momentum tensor of Callan, Coleman and Jackiw. Our methods also apply to
supersymmetric gauge theories with a Fayet-Iliopoulos term. We construct the
natural supercurrent multiplet for such a theory and show how to improve this
to a formally gauge-invariant Ferrara-Zumino multiplet by introducing a
non-dynamical chiral superfield S to ensure superfield gauge invariance.
Finally we study the coupling of this theory to supergravity and show that S
remains non-dynamical if the theory is R-symmetric and that S becomes
propagating if the theory is not R-symmetric, leading to non-minimal 16_B+16_F
supergravity.
