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Pseudo-bending is an algorithm for calculating seismic travel time through complex 3D velocity models. The algorithm was originally proposed by Um and Thurber (1987) and later extended by Zhao et al. (1992) to account for first order velocity discontinuities. We have modified Zhao's method of handling discontinuities by implementing a two-dimensional (2D) minimization algorithm that searches for the point on the velocity discontinuity surface where Snell's Law is satisfied. Further, our implementation reduces the likelihood that the pseudo-bending algorithm will return a local minimum by starting the ray calculation from several different starting rays. Specifically, interfaces are defined that include first order discontinuities plus additional interfaces at levels of the model where local minima might be generated. Rays are computed that are constrained to bottom in each layer between these interfaces. The computed rays might be reflected off the top of the layer, turn within the layer, or diffract along the interface at the bottom of the layer. The computed ray that is seismologically valid and that has the shortest travel time is retained. The modifications we have made to the algorithm have made it more accurate and robust but have also made it more computationally expensive. To mitigate this impact, we have implemented our software in a distributed parallel computing environment, which makes possible the calculation of many rays simultaneously.