Non-relativistic QCD (NRQCD) predicts colour octet contributions to be
significant not only in many production processes of heavy quarkonia but
also in their radiative decays. We investigate the photon energy
distributions in these processes in the endpoint region. There the velocity
expansion of NRQCD breaks down which requires a resummation of an infinite
class of colour octet operators to so-called shape functions. We model these
non-perturbative functions by the emission of a soft gluon cluster in the
initial state. We found that the spectrum in the endpoint region is poorly
understood if the values for the colour octet matrix elements are taken as
large as indicated from NRQCD scaling rules. Therefore the endpoint region
should not be taken into account for a fit of the strong coupling constant
at the scale of the heavy quark mass.