In accelerator projects involving the use of very short bunches, such as the Linac Coherent Light Source (LCLS)--where the rms bunch length in the undulator section is 30-microns--it appears that even submicron imperfections in the beam tube surface can generate an impedance that is unacceptably large. The authors consider two periodic models of an imperfect, rough surface, one with small rectangular corrugations, the other with smooth sinusoidal oscillations. They compare the impedance of these two models, and apply the results to the LCLS parameters.