  We perform a detailed study of the production of isolated prompt photons in
polarized hadronic collisions, in the centre-of-mass energy range relevant to
RHIC. We compare the results obtained for a traditional cone-isolation
prescription, with those obtained by imposing an isolation condition that
eliminates any contribution to the cross section from the fragmentation
mechanism. The latter prescription will allow us to present the first fully
consistent next-to-leading order calculation in polarized prompt-photon
production. We will discuss the theoretical uncertainties affecting the cross
section, addressing the issue of the reliability of the perturbative expansion,
for both inclusive isolated-photon and photon-plus-jet observables. Finally, we
will study the dependence of our predictions upon the polarized parton
densities, and the implications for the measurability of the gluon density.
