In this paper, we propose a new reversible watermarking of medical images for the applications in telemedicine. By using a bit-stream insertion scheme, the patient's information can be treated as a watermark and can be embedded into the bit-stream of a cover image for remote transmission. The proposed method simplifies the design of traditional image coding after a reversible watermarking. Experimental results show that the compression ratio can be achieved up to 3.025. The watermarking capacity can be obtained over 0.75 bpp for some common images. In addition, the watermark can be extracted exactly and the cover image can be reconstructed either in a lossless way or a lossy way. The obtained results also show the improvement with respect to previous works.