Excitation of high-phase-speed Dyakonov surface waves guided by a surface-relief grating made of a uniaxial dielectric material was theoretically studied using the rigorous coupled-wave approach for illumination by
p
- and/or
s
-polarized plane waves. The absorptance at a fixed value of the free-space wavelength was plotted against the polar angle of incidence, and absorptance peaks were correlated with the solution of the dispersion equation of the underlying canonical boundary-value problem for Dyakonov-surface-wave propagation. Both
p
- and
s
-polarized plane waves can excite the high-phase-speed Dyakonov surface waves. No, one, or multiple excitations of high-phase-speed Dyakonov surface waves are possible, depending upon the structural parameters of the grating. Excitation of a high-phase-speed Dyakonov surface wave as a specular Floquet harmonic also appears possible.