Parameterization via the bend locus curve allows optimization of single-spherical-bend lightpipes. It takes into account the bend radii, the bend ratio, allowable volume, thickness, and other terms. Parameterization of the lightpipe allows the inclusion of a constrained optimizer to maximize performance of the lightpipe. The simplex method is used for optimization. The standard and optimal simplex methods are used to maximize the standard Lambertian transmission of the lightpipe. A second case presents analogous results when the ray-sample weighted, peak-to-average irradiance uniformity is included with the static Lambertian transmission. These results are compared to a study of the constrained merit space. Results show that both optimizers can locate the optimal solution, but the optimal simplex method accomplishes such with a reduced number of ray-trace evaluations.