The variational methods employed by several writers are discussed, and their methods of choosing parameters in a trial wave function examined. It is pointed out that the parameters may be obtained in other ways, while still using the variation principle to compute an improved value of the asymptotic phase. The essentially equivalent process of perturbing a simple potential into the given form and evaluating the first order perturbation is also considered. The advantages and limitations of several methods proposed are examined numerically in a particular case of scattering by a Yukawa potential.