We study the feasibility of measuring the semi-exclusive photon production
gamma + p --> gamma + Y at HERA. The cross section of photons produced at l
arge transverse momenta, recoiling off an inclusive system Y of limited mas
s, can without photon isolation cuts simply be expressed in terms of hard P
QCD subprocesses and standard target parton distributions. With the help of
event generators we identify the kinematic region where quark and gluon fr
agmentation processes can be neglected. The cross section in this semi-excl
usive region is large enough to be measured with an upgraded HERA luminosit
y of L = 100 pb(-1). The subprocesses of lowest order in alpha (s) are supp
ressed at low recoil masses M-Y, compared to higher order gluon exchange, i
.e. BFKL contributions. The distinct M-Y-dependence makes it possible to de
termine experimentally the kinematic range where the higher order processes
dominate.