Structure, apparatus, and method for performing conservative hidden surface removal in a graphics processor. Culling is divided into two steps, a magnitude comparison content addressable memory cull operation (MCCAM Cull), and a subpixel cull operation. The MCCAM Cull discards primitives that are hidden completely by previously processed geometry. The Subpixel Cull takes the remaining primitives (which are partly or entirely visible), and determines the visible fragments. In one embodiment the method of performing hidden surface removal includes: selecting a current primitive comprising a plurality of stamps; comparing stamps to stamps from previously evaluated primitives; selecting a first stamp as a currently potentially visible stamp (CPVS) based on a relationship of depth states of samples in the first stamp with depth states of samples of previously evaluated stamps; comparing the CPVS to a second stamp; discarding the second stamp when no part of the second stamp would affect a final graphics display image based on the stamps that have been evaluated; discarding the CPVS and making the second stamp the CPVS, when the second stamp hides the CPVS; dispatching the CPVS and making the second stamp the CPVS when both the second stamp and the CPVS are at least partially visible in the final graphics display image; and dispatching the second stamp and the CPVS when the visibility of the second stamp and the CPVS depends on parameters evaluated later in the computer graphics pipeline.