Efficient shape representations are important for many image processing applications. Distance transform based algorithms can be used to compute the set of centres of maximal discs/spheres, that represents a shape. This paper describes a method that reduces this set, under the constraint that the shape can be exactly reconstructed using the reverse distance transformation. The reduced set can be used in the same ways as the ''standard'' set, e.g. for efficient storage, segmentation into parts of different thickness, shape manipulation, and skeletonization, all in 2D and 3D.