In this paper, we build multi-resolution source codes using entropy constrained dithered scalar quantizers. We demonstrate that for n-dimensional random vectors, dithering followed by uniform scalar quantization and then by entropy coding achieves performance close to the n-dimensional optimum for a multi-resolution source code. Based on this result, we propose a practical code design algorithm and compare its performance with that of the Set Partitioning in Hierarchical Trees (SPIHT) algorithm on natural images.