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Three-dimensional wavelet coding of volumetric medical images provides better coding performance compared to corresponding 2D methods by exploiting the inter-slice correlation that exists in such data. It introduces however latencies when it comes to retrieving/transmitting specific parts of the volume. This paper presents an extension to 3D-SPIHT which allows 3D region of interest (ROI) coding. ROI coding enables faster reconstruction of diagnostically useful regions in volumetric datasets by assigning higher priority to them in the bitstream. It also introduces the possibility for an increased compression performance, by allowing certain parts of the image to be coded in a lossy manner while others are coded losslessly. The necessary modifications to 3D-SPIHT for ROI coding are described and methods for specifying a 3D ROI without adding a significant overhead are suggested. Results are presented highlighting the benefits of the ROI extension.