Most wavelet-based image coders fail to model the joint coherent behavior of wavelet coefficients near edges. Wedgelets offer a convenient parameterization for the edges in an image, but they have yet to yield a viable compression algorithm. In this paper, we propose an extension of the zerotree-based Space-Frequency Quantization (SFQ) algorithm by adding a wedgelet symbol to its tree-pruning optimization. This incorporates wedgelets into a rate-distortion compression framework and allows simple, coherent descriptions of the wavelet coefficients near edges. The resulting method yields improved visual quality and increased compression efficiency over the standard SFQ technique.