In this paper, we present a new approach to conservative bounding of displaced Bézier patches. These surfaces are expected to be a common use case for tessellation in interactive and real-time rendering. Our algorithm combines efficient normal bounding techniques, min-max mipmap hierarchies and oriented bounding boxes. This results in substantially faster convergence for the bounding volumes of displaced surfaces, prior to tessellation and displacement shading. Our work can be used for different types of culling, ray tracing, and to sort higher order primitives in tiling architectures. For our hull shader implementation, we report performance benefits even for moderate tessellation rates.