In this paper, on the basis of the concept of the impedance purtubation, the principle of invariance of the square of the coupling cofficients proved by Unger is generalized. With this generalization, it becomes simpler to compute the random tolerances with small correlation distance and the discrete tolerances. Unified formulas are derived for computation of various tolerances of waveguides. In addition, relations between relevant pairs of coupling coefficients are obtained.The added attenuation due to an arbitrary form of uniform irregularity is expressed in terms of the maximum allowed impedance perturbation.Numerical examples are given.