Two common approaches have been developed to compress volumetric medical data from sources such as magnetic resonance imaging (MRI) and computed tomography (CT): (1) 2D-based compression methods, which compress each image slice independently using 2D image codecs; and (2) 3D-based compression methods, which treat the data as true volumetric data and compress using 3D image codecs. It has been shown that most 3D-based compression methods, such as 3D-SPIHT, can achieve significantly higher compression quality than most 2D-based compression methods, such as JPEG, JPEG-2000, and 2D-SPIHT. However, the compression/decompression speed is slow, and the high computational complexity and high memory usage render 3D-based compressions difficult to implement in hardware. In this paper, we propose a new 3D-based compression algorithm, 3D-BCWT, which is an extension to the computationally efficient BCWT (Backward Coding of Wavelet Trees) algorithm . 3D-BCWT not only can achieve the same high compression quality as 3D-SPIHT does, but it can also provide extremely fast compression/decompression speed, low complexity, and low memory usage, which are ideal for low-cost hardware and software implementations and for compressing high resolution volumetric data. Moreover, 3D-BCWT also possesses the capabilities of progressive transmission and decoding, such as progression of resolution and progression of quality, which are essential features for efficient image retrieval from large online archives.