The tightness of the bounding volume is often difficult to adjust to suit different applications. In this paper, we present a technique to derive a tunable bounding volume for elliptic paraboloids, where the tightness can easily be controlled and altered at several levels. Our technique develops such a tunable bounding volume through the optimization process. Bounding volumes thus developed contain the minimal volume at the corresponding level. We implement a geometric application for the elliptic paraboloid, and analyze the tightness of the bounding volumes at different levels. Finally, we demonstrate the feasibility of using our technique in creating new types of geometries as well as several rendered images.