The canonical boundary-value problem for Dyakonov-surface-wave propagation in a fixed direction guided by the planar interface of a uniaxial dielectric material and an isotropic nondissipative dielectric material was solved. Both partnering materials were taken to be homogeneous and the constitutive parameters for both to lie within the ranges of available materials. Solutions were found for which the phase speed of the Dyakonov surface wave is greater than the phase speed of a plane wave in the bulk isotropic partnering material.