New techniques for redundancy removal of quantized coefficients of a wavelet transform are discussed. Several strategies are developed to improve the redundancy reduction stage in subband/wavelet based image compression. The influence of the scanning path in coding the coefficients of the subbands after transformation are pointed out and solutions are proposed for exploiting the correlation between the coefficients in a more efficient way. New methods are also proposed to encode the address of non zero coefficients using blocks in both the lossy and lossless approach. Simulations show a better performance of the proposed techniques when compared to classical methods, while maintaining an efficient implementation complexity.