Experiments with a multidimensional nano-contact system (Lucas, Hay, and Oliver, J. Mater. Res. 2004) have shown that, prior to kinetic frictional sliding, there is a significant reduction of the tangential contact stiffness relative to the elastic prediction. The reduction occurs at contact sizes below about 50~200nm for aluminum single crystals and several other materials. Using a cohesive interface model, we find that this reduction corresponds to a transition from a small-scale-slip to large-scale-slip condition of the interface.