A coaxial metal rod with partial dielectric coating is considered as a means for efficient suppression of all volume competing modes in cavities for second-harmonic gyrotrons operated in whispering gallery modes. The rod radius is selected small enough to have only a slight effect on operating mode, which therefore remains insensitive to fabrication tolerances and a misalignment of the coaxial insert. By contrast, for the competing modes such a rod is shown to reduce the effective cavity length, thereby greatly increasing the starting currents. Such a method of mode selection is demonstrated to be more versatile, when compared to that provided by a tapered coaxial conductor. The advantage of a dielectric-coated coaxial insert is illustrated by the example of a cavity for a 100-kW 300-GHz pulsed gyrotron operated in the second-harmonic mode.