The transport characteristics of pure narrow 2D conductors, in which the electron scattering is caused by rough side boundaries, have been studied. The conductance of such strips is highly sensitive to the intercorrelation properties of inhomogeneities of the opposite edges. The case with completely correlated statistically identical boundaries (CCB) is a peculiar one. Herein the electron scattering is uniquely due to fluctuations of the asperity slope and is not related to the strip width fluctuations. Owing to this, the electron relaxation lengths, and specifically the localization length, depend quite differently on the asperity parameters as compared to the case for conductors with arbitrarily intercorrelated edges. A method for calculating the dynamical characteristics of the CCB electron waveguides is proposed clear of any restrictions on the asperity height.