A combination of trellis coded quantization (TCQ) and its vector alphabet generalization TCVQ is used to code the coefficients resulting from a biorthogonal wavelet transform in an image. TCVQ is a vector trellis coder with fixed rate, very good rate-distortion performance, and yet reasonable implementation complexity. The experimental results show that the Lena image can be coded by this coding system at the rate of 0.265 bpp to yield a peak signal-to-noise ratio (PSNR) of about 29 dB. This PSNR is about 3 dB larger than that obtained by a coding system of the same rate that uses VQ to obtain the wavelet transform coefficients. Naturally, the performance of the TCQ/TCVQ wavelet transform coder can be improved if entropy-coded TCQ and TCVQ coders are employed.