Occlusion-compatible traversals and z-buffering are often regarded as the only choices for resolving visibility in the image- and point-based rendering community. These algorithms do either per-frame or per-pixel computations. This paper first discusses visibility orderings for point samples in general and then discusses orderings that are valid for multiple views. Then we present a novel, highly efficient, visibility algorithm for point-sampled models that has much smaller per-frame cost than previous approaches. We also discuss a high-performance, cache friendly implementation of this visibility method and present results. Finally, we speculate on possible hardware implementations.