We calculate, to the next to leading order, the bremsstrahlung contrib
ution to the inclusive prompt-photon cross section in hadron-hadron co
llisions. We discuss the possible inputs for the parton-into-photon fr
agmentation functions, as well as the fragmentation scale dependence o
f the full inclusive next to leading order prediction. The effect of t
hese corrections is shown to be quite significant in the small-x(t) ra
nge, x(t) approximately O(10(-2) at collider energies, and the importa
nce of the gluon into photon fragmentation process is stressed.