  We study the feasibility of measuring semi-exclusive photon production \gamma
+ p \to \gamma + Y at HERA. The cross section of photons produced at large
transverse momenta, recoiling off an inclusive system Y of limited mass, can
without photon isolation cuts be simply expressed in terms of hard pQCD
subprocesses and standard target parton distributions. With the help of event
generators we identify the kinematic region where quark and gluon fragmentation
processes can be neglected. The cross section in this semi-exclusive region is
large enough to be measured with an upgraded HERA luminosity of L = 100/pb. The
subprocesses of lowest order in \alpha_s are suppressed 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 determine experimentally the
kinematic range where the higher order processes dominate.
