This paper presents the use of combination of three methods for calculation and synthesis of high-efficiency microwave mode converters, such as radiators of gyrotrons. The analytical method yields immediate estimates of mode converter dimensions, the Scalar Integral Equation (SIE) allows one to synthesize efficiently the optimal profile of the mode converter, and the most accurate Electric Field Integral Equation (EFIE) is used to check all transmission characteristics of the converter including calculations of reflection and cross-polarization. The combination of these three methods is an optimal for the mode converter design. Just so the launcher was designed for a quasi-optical mode converter used in the 60 GHz gyrotron in the TE7,3 operating mode. The simulation results agree well with the measured data. The paper also presents for the first time an accurate derivation of the SIE method.