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In this paper, we present a lossy compression scheme based on the application of the 3D fast wavelet transform to code medical video. This type of video has special features, such as its representation in gray scale, its very few interframe variations, and the quality requirements of the reconstructed images. These characteristics as well as the social impact of the desired applications demand a design and implementation of coding schemes especially oriented to exploit them. We analyze different parameters of the codification process, such as the utilization of different wavelets functions, the number of steps the wavelet function is applied to, the way the thresholds are chosen, and the selected methods in the quantization and entropy encoder. In order to enhance our original encoder, we propose several improvements in the entropy encoder: 3D-conscious run-length, hexadecimal coding and the application of arithmetic coding instead of Huffman. Our coder achieves a good trade-off between compression ratio and quality of the reconstructed video. We have also compared our scheme with MPEG-2 and EZW, obtaining better compression ratios up to 119% and 46%, respectively for the same PSNR.