The "width and shift" operator occurring in a previously developed unified theory of Stark broadening by plasma electrons is approximated by different expressions which include time ordering to various orders (up to order four). For the special case of the Lyman-a line in the dipole approximation results also including time ordering to all orders are calculated and compared to the approximate results. Numerical evaluations for this case are presented using the wing expression of the unified theory. A particularly good agreement with the exact profile is obtained for an approximation which maintains time ordering to fourth order. As for the accuracy of un-time-ordered profiles, our results are less optimistic than those of Godfrey et al. The role of an accurate thermal average concerning the effect of time ordering is emphasized.