The study of planetary atmospheric atomic and molecular (resonance) line emissions often require sophisticated radiative transfer models to properly account for scattering and absorption effects. In this work a relatively new and simple, yet powerful, numerical technique for solving radiative transfer problems has been developed and coded for a two-level atom in a one-dimensional Cartesian coordinate system. Angular scattering is assumed to be isotropic, and the method has been tested for monochromatic, complete frequency redistribution, and angle-averaged frequency redistribution. Formally, the solution is based on the commonly known lambda operator method. Rapid and robust convergence is attained using an intermediate operator that is readily evaluated. In addition, bilinear extrapolation based on previous iterates is found to further increase the rate of convergence. The one-dimensional model intensity versus frequency profiles are found to compare favorably with those of other proven models over a large range of optical depths. ¿ American Geophysical Union 1994