Abstract: Non-photorealistic (illustrative) rendering augments typical rendering models to selectively emphasize or de-emphasize specific structures of rendered objects. Illustrative techniques may affect not only the rendering style of specific portions of an object but also their visibility, ensuring that less important regions do not occlude more important ones. Cutaway views completely remove occluding, unimportant structures-possibly also removing valuable context information-while existing solutions for smooth reduction of occlusion based on importance lack precise visibility control, simplicity and generality. We introduce a new front-to-back fragment composition equation that directly takes into account a measure of sample importance and allows smooth and precise importance-based visibility control. We demonstrate the generality of our composition equation with several illustrative effects, which were obtained by using a set of importance measures calculated on the fly or defined by the user. The presented composition method is suitable for direct volume rendering as well as rendering of layered 3D models. We discuss both cases and show examples, though focusing mainly on illustration of volumetric data.