The KIVA family of codes (Amsden et al., 1989,1993,1997) are being used by many researchers for internal combustion engine simulation. For these codes to continue to be useful, improvements need to be made to make them more efficient. One of the most CPU intensive parts of these codes is the pressure solver. Improvement in the convergence of the pressure solver could have a significant effect on the performance of the overall code. This paper presents the theory behind the matrix solution procedure utilized by KIVA. A different approach to preconditioning is then presented. When implemented, it is shown that the overall CPU time required to perform a simulation is reduced by up to 20% for pressure dominated three-dimensional simulations. This is accomplished without an increase in memory allocation.