A second-order perturbation solution describing the radial transport of a reactive species and concurrent deposition on wafer surfaces is derived for use in optimizing chemical vapor deposition process conditions. The result is applicable to various deposition reactions and accounts for both diffusive and advective transport, as well as both ordinary and Knudsen diffusion. Based on the first-order approximation, the deposition rate is maximized subject to a constraint on the radial uniformity of the deposition rate. For a fixed reactant mole fraction, the optimum pressure and optimum temperature are obtained using the method of Lagrange multipliers. This yields a weak one-sided maximum; deposition rates fall as pressures are reduced but remain nearly constant at all pressures above the optimum value. The deposition rate is also maximized subject to dual constraints on the uniformity and particle nucleation rate. In this case, the optimum pressure, optimum temperature, and optimum reactant fraction are similarly obtained, and the resulting maximum deposition rate is well defined.