A ring laser with a beam splitter, an external reverse wave suppressor mirror, and an internal two-way coupling mirror exhibits both traveling wave and standing wave characteristics. A simple 1-D model of this hybrid laser is used to find the frequencies and losses of the steady state longitudinal modes, which depend on the mirror reflectivities and separations in an intricate manner. Adjustment of the suppressor position on a fine scale yields markedly different results for various coarse positions if the internal mirror provides adequate coupling into the reverse wave.