This paper presents a novel still image compression scheme that extends the traditional JPEG standard with lossy-to-lossless compression support. The system follows a two-layer design approach which allows for backward compatibility with the conventional JPEG standard for the base layer and provides lossless compression when decoding the enhancement layer. The system employs several coding tools, including quadtree coding, spatial domain prediction, reversible discrete cosine transforms, and context-based arithmetic coding to efficiently encode losslessly the enhancement layer. Performance evaluations using a standard JPEG set of images show that the proposed system yields similar lossless compression performance to the state-of-the-art single-layer JPEG-LS standard while providing quality scalability and a JPEG-compatible base layer at the same time.