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A systematic approach to customising Homogeneous Multi-Processor (HoMP) architectures is described. The approach involves a novel design space exploration tool and a parameterisable system model. Post-fabrication customisation options for using reconfigurable logic with a HoMP are classified. The adoption of the approach in exploring pre- and post-fabrication customisation options to optimise an architecture's critical paths is then described. The approach and steps are demonstrated using the architecture of a graphics processor. We also analyse on-chip and off-chip memory access for systems with one or more processing elements (PEs), and study the impact of the number of threads per PE on the amount of off-chip memory access and the number of cycles for each output. It is shown that post-fabrication customisation of a graphics processor can provide up to four times performance improvement for negligible area cost.