A graphics processing pipeline (30) includes a programmable fragment shader (40) that is operable to, in response to a “test” instruction included in a fragment shader program that it is executing, trigger, if appropriate, the performance of an alpha-to-coverage operation (41), a late stencil test (42), and a late depth test (43) for a fragment being processed, and to then return updated coverage information to the fragment shader (40). This allows alpha-to-coverage and late stencil and depth test operations to be triggered and performed during shader execution, rather than having to wait until shader execution has been completed before performing those operations.