Interactions between two colliding spin-one-half radicals with nearly parallel Z projections are considered in the case of strong Heisenberg spin exchange. The average value of the transverse spin polarization is shown to distribute equally between interacting radicals after the collisions. This is equivalent to the exchange of the polarization in 50% of the collisions. Collisions between parallel spins are shown not to represent a kinetic bottleneck when spectral narrowing follows from electron spin exchange. Thus, in applying the Kubo-Anderson model to the system of interacting radicals, every spin collision, regardless of spin orientation, results in random movement among various sites of different resonant frequencies and thus to spectral narrowing. We conclude that limiting discussions of spin exchange to antiparallel spins and mutual spin flips may lead to a false impression of spin dynamics and spectral narrowing by Heisenberg spin exchange. (C) 2003 American Institute of Physics.