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A cylindrical waveguide provided with wedge-shaped metal vanes projecting radially inward from the wall of the guide and excited in the transverse-electric mode was analyzed for the cold (beam-absent) dispersion relation. The angular harmonics generated due to the angular periodicity of vanes were taken into account in the cold analysis. The results of the cold analysis of the vane-loaded structure with respect to the axial propagation constant and the cut-off frequency were plugged into the hot (beam-present) dispersion relation of a small-orbit gyro-traveling wave tube (gyro-TWT) in an otherwise smooth-wall waveguide to obtain the hot dispersion relation of a vane-loaded gyro-TWT. The latter was interpreted to obtain the Pierce-type small-signal gain equation of a vane-loaded gyro-TWT. The vane-loaded gyro-TWT enjoys a higher gain than that of the smooth-wall. The beam position, as well as the beam harmonic mode number relative to the waveguide mode number, was optimized for the maximum device gain. The number, angular width, and radial height of vanes were optimized for large gain values without the sacrifice of bandwidth. The competition amongst the close-by waveguide modes was studied. The results obtained by the present analysis were compared with those of the others available in the literature.