In the past thirty years, numerical grid generation has been a bottleneck in the computational fluid dynamics process. Many current grid generation schemes require significant user interaction to robustly generate good computational grids. This paper presents a new method to generate grids that combines hyperbolic grid generation with elliptic grid generation. The new scheme builds upon the strengths of the separate techniques by first applying hyperbolic grid generation, which is very fast but sometimes fails in strong concavities, and then using elliptic grid generation to locally fix the problems where hyperbolic grid generation fails. The new technique is demonstrated on a variety of cases that are known to cause problems for either hyperbolic grid generation or elliptic grid generation when applied alone.