The Anisotropic Source-Flux Iteration Technique (ASFIT) is a semianalytical method based on collision probabilities for energy-dependent radiation transport. In its original form, the coupled integral equations for space and energy-angle transmission were solved using discrete ordinate representation in space and energy and polynomial approximation in direction cosine for radiation flux and source terms. In this Note, the following modifications of ASFIT are presented: 1. discrete ordinate representation in direction cosine 2. sequential integration in space 3. exponential transformation in space 4. multiple energy structure for neutron transport. The Note discusses the rationale for these modifications, and their effect on the speed of computation, convergence, and capabilities of the code.