Numerically optimized launchers for the quasi-optical output coupler of high power gyrotrons have been developed to provide RF beams with high Gaussian mode content. Generally, the profiles of numerically optimized launchers are quite complicated, so the improvement of their tolerance to fabrication errors is very important. In order to reduce the stray radiation generated by launchers with quite complicated wall profile, and also to reduce their sensitivity to fabrication errors, a method for the smoothing of the numerically optimized launcher wall has been developed at KIT, which is based on the spectrum reconstruction approach. As an example, a launcher designed for the KIT TE34,19-mode, 2 MW CW coaxial-cavity gyrotron has been investigated.