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The analysis of a coaxial waveguide resonator with its central conductor corrugated with wedge-shaped slots, considering space harmonic effects due to slot periodicity, was used to study the problem of mode competition in a gyrotron. A more positive slope of the plot of the eigenvalue versus the ratio of the waveguide wall to outer slot radii (coaxial parameter) for the desired mode, typically, TE8,4 as compared to the corresponding slopes for the competing modes formed a basis for the study of mode separation. Considering the aspect of mode separation on the basis of the relative slopes of the eigenvalue plot and that of mode degeneracy, a tradeoff was made to select the slot depth at a value intermediate between the values corresponding to the narrow and deeper slots. For the slot depth parameter selected, one may find the coaxial parameter, around which to taper the structure cross section, for mode separation on the basis of relative slopes of the eigenvalue plot, avoiding, at the same time, the region of the mode degeneracy. The analysis and interpretation of results for mode separation with reference to the typical mode TE8,4 chosen is extendible to higher modes as well, which was exemplified with reference to the typical higher order TE12,4 and TE27,11 modes.