In the field of constitutive modelling of soil behaviour, optimisation techniques have been mostly employed as a calibration tool, particularly when several model parameters lack clear physical meaning. In this paper, however, a procedure based on a Hill-Climbing optimisation algorithm is presented as a form of improving the performance of constitutive models. Specifically, a simple cyclic nonlinear elastic model, which is shown to be unable to simulate adequately the damping ratio measured under small and large strain amplitudes, is modified by applying the Hill-Climbing technique to the determination of a new relationship describing the unloading/reloading behaviour of soil under cyclic loading. The performance of the proposed model is assessed by evaluating its parameters based on three distinct sets of empirical damping ratio curves and computing the corresponding error in their simulation. It is shown that the introduction of the new unloading/reloading expression formulated based on the outcome of the optimisation procedure increases substantially the precision of the constitutive model.