This paper deals with the design of a self-embedding scheme for JPEG-compressed images. Most of existing schemes are compatible only with loss-less images. Few of them are capable of handling lossy compression, but deliver very low restoration fidelity, and support only small amounts of tampered content. In this study, we extend a recently proposed self-embedding model, and perform theoretical analysis of the impact of watermark extraction and block classification errors on the achievable reconstruction performance. The theoretical results are verified experimentally with a new scheme dedicated to JPEG. Our scheme achieves the average reconstruction quality between 28 dB and 33 dB, for the maximum allowed tampering rates of 50% and 20%, respectively.