In a graphics processing system that includes one or more programmable shading stages, the shader compiler receives a shader program to be compiled (step 40), identifies any run time constant expressions in the shader program (step 41), and removes such expressions from the original shader program, and substitutes them in the original main shader program with appropriate load instructions pointing to where the output results from a pilot shader program will be stored (step 42). The shader compiler then creates a separate pilot shader program for the identified run-time constant expressions (step 43). The pilot shader program is then executed on the graphics processing pipeline (step 44), before the modified main shader program (step 45).