Three spatial differencing schemes to be used with the even-parity, discrete ordinates, neutron transport equations are presented for the case of slab geometry and isotropic scattering and sources. These three schemes are analyzed in accordance with several desirable properties for spatial differencing schemes. The analysis indicates that cell-edge differencing of the even-parity equations yields a second-order, positive method that satisfies most diffusion limits and leads to an iteration that can be readily accelerated with an effective diffusion synthetic algorithm. The analyses indicate that this approach is quite promising and should be further developed.