Edges are one of the most perceptually important features in images that provide geometric information to views to distinguish objects in a scene. Wavelet based coding algorithms have been successful in image compression, but like classical cosine transform methods, they are unable to provide a good representation of 2D edges. Cel-based animation sequences, or cartoons, contain predominantly edge information. Although these types of images are relatively less complex than real-life images, the geometrical structures within the cel images challenge even the most complex wavelet-based coders. Wedgelets and beamlets are able to capture geometrical structures in images more efficiently than wavelets. In this paper, we propose a novel hybrid image coder that utilises both wavelets and wedgelets to code cartoon images. Our prototype coder demonstrates significant improvements in visual quality of wedgelet/ beamlet coded cartoon images over standard wavelet-based coding techniques.