We consider the question of naturalness in supersymmetric theories, in view of constraints from flavour-changing processes, weak CP violation and rare decays. Since larger masses for the superpartners of ordinary fields improve the situation, we search for ways to increase the scale of supersymmetry breaking. Within the supersymmetric standard models, naturalness considerations prevent us from making these masses too large. However, if the gauginos are the heaviest supersymmetric partners at a high-energy scale, renormalization group evolution to the Weinberg-Salam scale leads to some degeneracy of scalar masses and thus some suppression of flavour-changing processes. Weak CP violation constraints, however, are rather restrictive. In a supersymmetric technicolor model with fundamental bosons, we can further raise the supersymmetry-breaking scale. Consequently, it is easier to satisfy the constraints from rare processes. In this theory, supersymmetry might be difficult to observe at SSC energies but other relatively light states are predicted.