The normal calculations of disadvantage factors in slab geometry are performed with the odd-order spherical harmonics approximations; however, by the use of the complementary even-order results in conjunction with these standard solutions, a more accurate answer can be quickly obtained. Since the even-order approximations give an apparent upper bound on the true answer, a combination of low odd and even-order solutions produces a counterconvergence effect which closely brackets the true disadvantage factor. In particular the theory of the P4 calculation is presented along with various numerical parameter studies.