In a narrowband 2-port resonator on 37°-cut quartz with Al electrodes (h(Alu) = 100 nm) exploiting surface transverse waves (STW), we have observed parasitic ripples which have been attributed to transverse modes unusually situated on the left side of the main resonance. To suppress these modes, we have used metallization coefficient weighting across the aperture, with more metal in the middle and reduced metallization close to the busbars. The parasitic modes indeed disappeared, but at significantly higher frequency, we have found an additional strong response which does not exist in a resonator with uniform electrode metallization. 3-D simulations showed that the structure has another very different mode, with the wave propagating mainly along the edge of the busbars, but excited with the interdigital electrode system.