Laterally excited bulk acoustic resonators (XBARs) are plate mode resonators in which one of the higher-order plate modes transforms into the bulk acoustic wave (BAW) due to the very thin plates used in these devices. The propagation of the primary mode is usually accompanied by numerous spurious modes, which deteriorate resonator performances and restrict potential XBARs' applications. This article suggests a combination of different methods for insight into the nature of the spurious modes and their suppression. Analysis of the BAW slowness surface provides optimization of XBARs for single-mode performance in the filter passband and around it. The rigorous simulation of admittance functions in the optimal structures allows for further optimization of electrode thickness and duty factor. Finally, the nature of different plate modes generated in a wide frequency range is clarified via simulation of dispersion curves, which characterize acoustic mode propagation in a thin plate under the periodic metal grating, and visualization of displacements accompanying wave propagation. Application of this analysis to lithium niobate (LN)-based XBARs demonstrated that in LN cuts with Euler angles (0°, 4°-15°, 90°) and plate thickness dependent on orientation and varying between 0.05 and 0.1 wavelengths, the spurious-free response could be achieved. Due to tangential velocities of 18-37 km/s combined with the coupling of 15%-17% and feasible duty factor a/p = 0.5, the found XBAR structures can be applied in high-performance 3-6 GHz filters.