One embodiment of the present invention includes techniques for rasterizing geometries. First, a processing unit defines a bounding primitive that covers the geometry and does not include any internal edges. If the bounding primitive intersects any enabled clip plane, then the processing unit generates fragments to fill a current viewport. Alternatively, the processing unit generates fragments to fill the bounding primitive. Because the rasterized region includes no internal edges, conflation artifacts caused when the number of coverage samples per pixel exceeds the number of color samples per pixel may be reduced. In prior-art techniques, reducing such conflation artifacts typically involves increasing the number of color samples per pixel to equal the number of coverage samples per pixel. Consequently, the disclosed techniques enable rendering using algorithms that reduce the ratio of color to coverage samples, thereby decreasing memory consumption and memory bandwidth use, without causing conflation artifacts associated with cover geometries.