Method for making containers having enhanced emptying capability include a filling/emptying opening disposed closely adjacent the container sidewall and extending through integral top closure structure. The container sidewall has a portion contiguous with the filling/emptying opening which extends therefrom without radial step discontinuity, thus avoiding well formation adjacent the opening. A parison is stretched unidirectionally and transversely against restraint by a blow pin to avoid buildup of material in the sidewall portion contiguous with the filling/emptying opening and the stretched parison is blow molded to form the container.