The computational requirements of full global illumination rendering are such that it is still not possible to achieve high-fidelity graphics of very complex scenes in a reasonable time on a single computer. By identifying which computations are more relevant to the desired quality of the solution, selective rendering can significantly reduce rendering times. In this paper we present a novel component-based selective rendering system in which the quality of every image, and indeed every pixel, can be controlled by means of a component regular expression crex. The crex provides a flexible mechanism for controlling which components are rendered and in which order. It can be used as a strategy for directing the light transport within a scene and also in a progressive rendering framework. Furthermore, the crex can be combined with visual perception techniques to reduce rendering computation times without compromising the perceived visual quality. By means of a psychophysical experiment we demonstrate how the crex can be successfully used in such a perceptual rendering framework. In addition, we show how the \crex's flexibility enables it to be incorporated in a predictive framework for time-constrained rendering.