In photonic crystal (PC) gratings whose structural symmetry is broken owing to one-side corrugations, the Rayleigh-Wood anomalies can appear in a one-way manner. In the combination with the vanishing coupling to the lowest Floquet-Bloch mode at the upper band edge, these anomalies lead to the appearance of the defect-mode-like, i.e., very narrow one-way transmission, peak, which cannot appear in the corresponding slab of PC without corrugations. Such a sole peak can be transformed into a one-way transmission band with a desired width by varying angle of incidence. The nonoverlapping and thus switchable one-way (higher-order) and two-way (zero-order) transmission bands can be obtained in both the frequency and incidence-angle domains. Adjustment of PC lattice and corrugation parameters allows one to obtain two subsequent one-way bands, every being connected with a certain higher diffraction order. Conditions required for the appearance of a narrow one-way transmission band in the vicinity of a Rayleigh-Wood anomaly are well consistent with typical dispersion features of a very large class of PCs and do not need unusual performances.