For pt.I, see ibid., vol.17, p.2599 (1984). General expressions for the line profile produced by an emitting atom embedded in a sea of randomly distributed identical perturbers, on the assumption that the interaction between the emitter and a perturber is of the type 1/Rp, were presented in Paper I. The basic assumptions of the theory are that all emitter-perturber interactions are additive and that the trajectory of the perturber is a straight line. The profile is expressed in terms of a 'universal' function that does not depend explicitly on any parameters associated with the particular spectral line or perturbing gas considered. Explicit results are given for the cases p=6 and p=7; these are relevant to the analysis of the broadening of atomic and molecular lines by atoms and molecules. For the case of p=6, the sensitivity of the line parameters to the direction assumed for the quantisation axis of the emitter is examined. It is also shown that the degree of asymmetry depends significantly upon the thermal average being correctly evaluated, and good agreement with experiment is obtained for the asymmetries of the sodium resonance lines perturbed by the heavier rare gases.