A system and a method are disclosed that reduce primitive overdraw in a GPU. An occlusion index (OI) for a first tile of a batch of graphical data. In one embodiment, the first tile is bypassed from an early coverage discard (ECD) first-in, first-out (FIFO) if the OI for the first tile is less than a first threshold, otherwise the first tile is entered into the ECD FIFO. The first tile is also bypassed from the ECD FIFO if the OI for the first tile is greater than a second threshold that is greater than the first threshold. In another embodiment, a queue length is logically changed for the first tile in the ECD FIFO if the OI for the first tile is greater than the first threshold and less than or equal to a third threshold that is greater than the first threshold and less than the second threshold.