Non-opaque primitives (e.g. translucent or punch-through primitives) often include some fragments which do not need to be treated as non-opaque fragments. For example, some fragments of a translucent primitive may be entirely opaque or entirely transparent. However, typically, the opacity states (e.g. alpha states) of the fragments are not known until texturing has been applied because it is the texture that includes the opacity information (e.g. the alpha values). However, as described herein, an opacity test is performed up front (e.g. before texturing is applied to fragments of a non-opaque primitive) to see if the processing of the fragments can be simplified. For example, if fragments are fully transparent then they may be discarded. As another example, if fragments are fully opaque then they may be handled as if they have an opaque object type such that the subsequent processing of the fragments is simplified.