It is proposed that importance sampling may be carried out using an approximate analytic form for the importance function. An altered Boltzmann kernel may then be computed. Choosing from this altered kernel is facilitated, in part, by particle splitting. The method is carried out in detail for neutron penetration in hydrogen slabs. Results are given for dose buildup and energy spectrum for slab depths up to 179 mean free paths for 8.1 Mev neutrons.