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Experiments on frequency step tuning have been performed in a coaxial cavity gyrotron equipped with a Brewster window. In single-mode operation, 19 different modes have been excited with high power In a frequency range between 134-169.5 GHz. In all modes, the radio frequency (RF) power was efficiently transmitted through the output window with only slightly varying RF power distribution. The step-frequency tuning is restricted by the coaxial insert. In particular, the strong increase of the quality factor for small values of the parameter w, which describes the corrugation impedance, limits the maximum frequency range. Furthermore, the increase of ohmic losses at the insert for modes with reduced caustic radius may restrict the selection of usable modes.