Gently sloped perturbation of the wall of a planar waveguide can lead to Wood's anomaly which realizes as disproportionately rapid changes of the diffraction pattern near thresholds. By means of an asymptotic analysis certain restrictions on the profile of the wall perturbations are found that provide the appearance of the anomaly, its sharpening or extinction. The asymptotics of eigenvalues is studied and complex and threshold resonances are discussed.