  We consider the prompt hadroproduction of J/psi, psi' and the Upsilon
(1S,2S,3S) states caused by the fusion of a symmetric colour-octet two-gluon
state and an additional gluon. The cross sections are calculated in
leading-order perturbative QCD. We find a considerable enhancement in
comparison with previous perturbative QCD predictions. Indeed, the resulting
cross sections are found to be consistent with the values measured at the
Tevatron and RHIC, without the need to invoke non-perturbative `colour-octet'
type of contributions.
