The effect of widely differing scattering laws on the critical thickness of a multiplying slab in one-speed neutron transport theory is studied using a scattering kernel which consists of a linear combination of backward, forward and isotropic scattering. An extensive numerical survey is carried out for the critical thickness in order to provide benchmark results for future studies. 'Exact' solutions are obtained by two methods: the Wiener-Hopf technique and the method of elementary solutions. Although both methods lead to the same results, it is shown that the method of elementary solutions is superior, in terms of operational simplicity, for this type of problem.