A combined analytical and numerical method is employed to optimize process conditions for composites fiber coating by chemical vapor infiltration. For a first-order deposition reaction, the optimum pressure yielding the maximum deposition rate at a preform center is obtained in closed form and is :found to depend only on the activation energy of the deposition reaction, the characteristic pore size, and properties of the reactant and product gases. It does not depend on the preform specific surface area, effective diffusivity or preform thickness, nor on the gas-phase yield of the deposition reaction. Further, this optimum pressure is unaltered by the additional constraint of a prescribed deposition uniformity Optimum temperatures are obtained using an analytical expression for the optimum value along with numerical solutions to the governing transport equations. These solutions account for both diffusive and advective transport, as well as both ordinary and Knudsen diffusion. Sample calculations are presented for coating preform fibers with boron nitride.