We propose and develop a novel rigorous technique that enables one to obtain the explicit numerical values of parameters at which several lowest-order harmonics of the scattered field are suppressed. This provides partial cloaking of the object, a perfectly conducting cylinder of circular cross section covered by two layers of dielectric separated by an infinitely thin impedance layer, a two-layer impedance Goubau line (GL). The developed approach is a rigorous method that enables one to obtain in the closed form (and without numerical calculations) the values of parameters providing the cloaking effect, achieved particularly in terms of the suppression of several scattered field harmonics and variation of the sheet impedance. This issue constitutes the novelty of the accomplished study. The elaborated technique could be applied to validate the results obtained by commercial solvers with virtually no limitations on the parameter ranges, i.e., use it as a benchmark. The determination of the cloaking parameters is straightforward and does not require computations. We perform comprehensive visualization and analysis of the achieved partial cloaking. The developed parameter-continuation technique enables one to increase the number of the suppressed scattered-field harmonics by appropriate choice of the impedance. The method can be extended to any dielectric-layered impedance structures possessing circular or planar symmetry.