Several techniques for acceleration of ray tracing parametric surfaces are presented. Some of these are entirely new to ray tracing, while others are improvements of previously known techniques. First a uniform spatial subdivision scheme is adapted to parametric surfaces. A new space- and time-efficient algorithm for finding raysurface intersections is introduced. It combines numerical and subdivision techniques, thus allowing utilization of ray coherence and greatly reducing the average ray-surface intersection time. Non-scanline sampling orders of the image plane are proposed that facilitate utilization of coherence. Finally, a method to handle reflected, refracted, and shadow rays in a more efficient manner is described. Results of timing tests indicating the efficiency of these techniques for various environments are presented.