Semiconductor lasers subject to optical feedback are of both scientific and technological importance. The laser and external mirror form a compound cavity which can be modeled using a coupled cavity approach. Using this approach we have calculated the longitudinal mode frequencies and the associated mode lifetimes of all the modes in the system. We have found that for a narrow range of external cavity reflectivities, the mode lifetimes become almost degenerate. In this regime the mode lifetimes become highly sensitive to variations in the refractive index of the laser and external cavity reflectivities. Close inspection of this regime has revealed ever finer detail, suggesting a fractal structure to the mode solutions. The calculations have been undertaken in the 'cold cavity' limit and indicate a catastrophic loss of mode discrimination, even in a system with no inherent material gain. In the short cavity limit the external reflectivity required to induce the loss of mode discrimination varies as a function of external cavity round-trip time.