The color-octet model has been used successfully to analyze many problems i
n heavy quarkonium production. We examine some of the conceptual and practi
cal problems of the soft gluon emission process in the color-octet model. W
e use a potential model to describe the initial and final states in the sof
t gluon emission process, as the emission occurs at a late stage, after the
production of the heavy quark pair. It is found in this model that the sof
t gluon M1 transition S-1(0)(8)-->S-3(1)(1) dominates over the E1 transitio
n P-3(J)(8)-->S-3(1)(1) for J/psi and psi' production. Such a dominance may
help resolve the questions of isotropic polarization and color-octet matri
x element universality in the color-octet model. [S0556-2821(99)03721-2].