  The hierarchy of long-distance matrix elements (MEs) for quarkonium
production depends on their scaling with the velocity $v$ of the heavy quark in
the bound state. Ranges for the velocities in various bound states and
uncertainties of colour-singlet MEs are estimated in a quark-potential model.
Different possibilities for the scaling with $v$ of the MEs are discussed; they
depend on the actual values of $v$ and the QCD scale. As an application, J/psi
polarization in e^+e^- annihilation is discussed. The first non-perturbative
estimates of colour-octet MEs are presented and compared with phenomenological
determinations. Finally, various predictions of prompt quarkonium production at
LEP are compared.
