This study used a computer simulation model to investigate various considerations that affect optimum peak height in a running jump. A planar eight-segment computer simulation model with extensor and flexor torque generators at five joints was formulated and customised to an elite male high jumper. A simulation was matched to a recorded high jumping performance by varying the activation profiles of each of the torque generators giving a simulated peak height of 1.99 m compared to the recorded performance of 2.01 m. In order to maximise the peak height reached by the mass centre in the flight phase, the activation profiles were varied, keeping the same initial conditions as in the matching simulation. Optimisations were carried out without any constraints, with constraints on the angular momentum at take-off, with further constraints on joint angles, and with additional requirements of robustness to perturbations of activation timings. A peak height of 2.37 m was achieved in the optimisation without constraints. Introducing the three constraints in turn resulted in peak heights of 2.21, 2.14 and 1.99 m. With all three types of constraints included, the peak height was similar to that achieved in the recorded performance. It is concluded that such considerations have a substantial influence on optimum technique and must be included in studies using optimised simulations.