The popular Tung model for Schottky barrier inhomogeneity considers how low-barrier patches (embedded in a high barrier background) impact the diode current. However, Tung's model fails to account for the image-force effect. We analyze how the image force alters the current through an inhomogeneous barrier and find that, in some circumstances, it will smooth the barrier, such that the current will effectively be that of a homogeneous diode. We also show that for a distribution of defect barriers and/or sizes, the diode current can be intermediate between that of a homogeneous diode and a diode dominated by the low-barrier patches. We calculate the parameter values associated with this transitional region. A survey of existing literature applications of Tung's model shows that many diodes are actually operating in this transition region, where Tung's equations are in error. We provide the corrected equations for this case and demonstrate their ability to model practical diode characteristics.