This work revisits the problem of ray effects in discrete ordinates calculations that frequently occurs in two- and three-dimensional systems which contain isolated sources within a highly absorbing medium. The effectiveness of using a first collision source or a second collision source are analyzed as possible remedies to mitigate this problem. The first and second scattering sources are calculated with the Monte Carlo method that is intrinsically free from ray effects. The scattering source is then coupled to a discrete ordinates code for a hopefully ray-effect-free transport calculation. The scattering source generated by the Monte Carlo method is distributed throughout geometry space and therefore would be less likely to produce ray effects in the discrete ordinates calculation. This remedy for the ray effect is demonstrated for a point source in cylindrical geometry and for a localized distributed source in X-Y geometry. The first collision and second collision sources are generated by three-dimensional Monte Carlo calculations and enables its application to a variety of source configurations and the results can be coupled to a two- or three-dimensional discrete ordinates transport code. The Monte Carlo computational time and precision requirements constitute some limitations but these are minimized since the Monte Carlo transport is performed only up to the first collision.