Rendering in computer graphics is the process of converting a three dimensional scene description into a two dimensional image. In this work we focus on high quality rendering, which has numerous applications in entertainment and visualization. Many films today are created either entirely or in concert with computationally generated imagery and serve as a vivid example of the benefits of high quality rendering. This dissertation consists of two parts, each presenting novel work in the field of high quality, high performance rendering. The first part proposes the use of volumetric occluders, or a collection of axis-aligned boxes placed within a polygonal model, to accelerate the rendering of shadows cast by the model while producing images identical to the unaccelerated baseline. We show that our approach performs well on single object scenes and extend our approach for use with scenes from a professional open source movie. Although the technique has not yet proven itself on these multi-object scenes, we identify the scene characteristics which are hampering the approach and show that in some cases it is still possible to achieve an improvement in performance. The second part of the dissertation presents a new way to determine micropolygon tessellation rate within a Reyes style renderer. Our new scheme, called final approach tessellation, evaluates the tessellation rate close to a Reyes surface rather than upon entry into its bounding box. Our determination of the tessellation rate is more aggressive than previous approaches, producing a more compact tessellation which in turn is faster to compute and requires less memory. Our evaluation shows that although final approach tessellation is promising in theory, it ultimately fails to improve performance on actual test scenes. / text