Abstract-The process before quantization stage in compression process is a very crucial stage espeacially in application that require a high compression ratios. So, in this paper, we propose a new method of image compression that is based on reducing the wavelet coefficients in wavelet details subbands. It is based on the concept of local subband wavelet coefficients minimization to find the optimum threshold value for wavelet coefficients in each detail subbands. The proposed method decomposed the image into LL (low resolution approximate image), HL (intensity variation along column, horizontal edge), LH (intensity variation along row, vertical edge) and HH (intensity variation along diagonal). The coefficients in details subband retrived from the decomposition process is then manipulated in such a way that the nearly zero coefficient is discarded while the rest is remained. This process will reduce the unsignificant wavelet coefficient that leads to a great compression ratio while preserving the informative data to produce a good image quality as can be seen in the experiment done.