In this paper, a fragment-processing solution in 3D graphics rendering algorithms based on fragment lists (i.e. A-buffer) for minimizing loss of image quality is described. While all fragment information should be preserved for exact hidden surface removal, this places additional strain on hardware in terms of silicon gates and clock cycles. Therefore, we propose a fragment processing technique that can effectively merge fragments in order to decrease the depth of fragment lists. It renders scenes quite accurately even in the case when three fragments intersect each other. This algorithm improves hardware acceleration without deteriorating image quality.