Abstract: Bounding volumes are usually employed to accelerate computing for complex geometries. In this paper, we present a technique to derive a tunable bounding volume for an elliptic paraboloid, given a parameter related to the tightness. Each bounding volume thus developed is sufficiently tight to the original elliptic paraboloid under a user`s control. This tunable feature helps us selecting the most suitable bounding volume. It also contributes to achieve a balance between the computing efficiency and inherent overheads for bounding volumes. We implemented our technique in Monte Carlo applications where an elliptical paraboloid is considered as a luminaire for direct illumination and global illumination calculations. Experimental results verify the effectiveness of our technique.