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Many applications require operations on multiple fragments that result from ray casting at the same pixel location. To this end, several approaches have been introduced that process for each pixel one or more fragments per rendering pass, so as to produce a multifragment effect. However, multifragment rasterization is susceptible to flickering artifacts when two or more visible fragments of the scene have identical depth values. This phenomenon is called coplanarity or Z-fighting and incurs various unpleasant and unintuitive results when rendering complex multilayer scenes. In this work, we develop depth-fighting aware algorithms for reducing, eliminating and/or detecting related flaws in scenes suffering from duplicate geometry. We adapt previously presented single and multipass rendering methods, providing alternatives for both commodity and modern graphics hardware. We report on the efficiency and robustness of all these alternatives and provide comprehensive comparison results. Finally, visual results are offered illustrating the effectiveness of our variants for a number of applications where depth accuracy and order are of critical importance.