Point-based rendering is a compact and efficient means of displaying complex geometry. Our goal is to enable flexible point-based rendering, permitting local image refinement, required for example when zooming into very complex scenes, and efficient shadow computations. We use hierarchical packed point representations, based on recursive grid data structures. Such compact structures are particularly well adapted to devices with limited memory and display resolution, such as PDA's. To achieve flexible rendering we store intermediate attributes such as normals and colors at internal nodes of the hierarchy. We examine the memory and computation tradeoffs involved in the type of structure used, and find that tri-grids (3x3x3 hierarchical grids) are a suitable compromise for many cases. We show implementations of our method on PC and on a PDA,