Three-dimensional image compression methods outperform their two-dimensional counterparts in the sense of higher rate-distortion performance for compressing volumetric image data. The state-of-the-art transform-based 3D compressors, such as 3D-SPIHT and 3D-DCT, are characterized for their rate control ability, where the qualities of the image, although are adjustable with respect to rates, are not explicitly controllable. A novel method, based on vector quantization in an enhanced image pyramid with error feedback, has been proposed, where the quality of the decompressed image only depends on the encoding of coefficients from the finest band and therefore a distortionconstraint transform coding is achieved. Compared to the previous image pyramid transform coders, its coding efficiency has been improved by using a cross-band classified vector quantizer (CBCVQ), where the encoding of current band will benefit from the encoding result from previous bands. Two explicit bit-allocation schemes, one is regarding the bit allocation across bands and the other is across the sub vector quantizers within each band, have been applied to minimize the total rate under the constraint of specified distortion. Evaluations have been performed on several data sets obtained by confocal laser scanning microscopy (CLSM) scans for vascular remodeling study. The results show that the proposed method has competitive compression performance for volumetric microscopic images, compared to other state-of-the-art methods. Moreover the distortion-constraint feature offers more flexible control than its rate-constraint counterpart in bio-medical image applications. Additionally, it effectively reduces the artefacts presented in other approaches at low bit rates and therefore achieved more subjective acceptance.