Recently, a number of variable impedance actuator designs have been proposed under different motivations (safe human-robot interaction, mechanical robustness and energy storing to cite a few). In a recent paper (Berret et al. (2011)) we observed that none of the available designs seem to reproduce an important characteristic of human muscles, i.e. the ability to open-loop reject disturbances by means of muscle co-activation. Starting form this observation, we recently designed a novel single-joint actuator (nr-VIA) based on the use of non-linear springs in agonistantagonist configuration. In this paper we discuss some control related characteristics of the proposed design. The theoretical analysis is conducted without specifying the potential energy of the springs. We first design a control law capable of monotonically increasing the joint-stiffness (i.e. disturbance rejection) without changing the joint equilibrium configuration; this result is obtained with minimal requirements on the potential energy of the springs. The same control law is then proven (under more restrictive conditions) to monotonically decrease the sensitivity of the joint equilibrium with respect to the actuation variables, a desirable property when trying to achieve a finer control over joint positioning.