  Exclusive processes at large momentum transfer Q factor into perturbatively
calculable short-distance parts and long-distance hadronic wave functions.
Usually, only contributions from the leading Fock states have to be included to
leading order in 1/Q. We show that for exclusive decays of P-wave quarkonia the
contribution from the next-higher Fock state |Q Qbar g> contributes at the same
order in 1/Q. We investigate how the constituent gluon attaches to the hard
process in order to form colour-singlet final-state hadrons and argue that a
single additional long-distance factor is sufficient to parametrize the size of
its contribution. Incorporating transverse degrees of freedom and Sudakov
factors, our results are perturbatively stable in the sense that soft
phase-space contributions are largely suppressed. Explicit calculations yield
good agreement with data on chi_{c J} decays into pairs of pions, kaons, and
etas. We also comment on J/psi decays into two pions.
