A method and apparatus for determining and utilizing Z values of fragments in an anti-aliasing video graphics system is described. This method and apparatus are accomplished by sampling the fragment to produce a plurality of samples where a valid sample indicate coverage of a pixel by the fragment at a portion of the pixel corresponding to the valid sample. The Z value of a front-most valid sample of the plurality of samples is then determined. This Z value is preferably determined by determining the Z value at a reference point within the pixel and then ranking the various samples based on their positions and the slopes of the Z value in the horizontal and vertical directions with respect to the reference point. The highest ranked sample that is a valid sample is then selected, and the Z value for that sample is calculated based on the Z value at the reference point, the position of the selected sample with respect to the reference point, and the slopes. Once the Z value of the front-most sample of the plurality of samples has been determined, this Z value is used as the Z value for all of the valid samples within the fragment.