Extraordinary optoconductance (EOC) devices with symmetric leads have been shown to have a symmetric positional dependence when exposed to focused illumination. While advantageous for a position sensitive detector (PSD), this symmetric positional dependence, when the device is uniformly illuminated, leads to a minimization of the output voltage. Here, with the aid of a previously employed point charge model, we address two ways to break the symmetry and recover the output signal. The first is to impose uniform illumination but only on half the sample. This method has practical limitations as the device is miniaturized to the nanoscale. The second is via asymmetric placement of the voltage probes in a four-probe measurement. Crucial to the discussion is the effect of the surface charge density. Several ways of modeling the induced surface charge density are presented. Utilizing the above described approach, optimal asymmetric lead positions are found.