The specification describes dispersion compensators that are adjustable based on selection of mode propagation properties of two or more modes. The fundamental device structure comprises two or more sections of optical fiber that support the fundamental mode as well as well as one or more higher-order-modes (HOM). The HOM fibers are connected to each other by means of a spatial mode-converter (MC) that is switchable. The MC may be fabricated with, for example, long-period fiber-gratings (LPG), coupled waveguide devices, free-space phase-retardation elements, micro-electro-mechanical devices, or acousto-optic couplers. The MC is assembled such that it transforms any incoming spatial mode into one of any other guided modes in the HOM fiber. Switching is achieved by strain, temperature, the electro-optic or nonlinear optic effect, or any other physical effect that changes the refractive index of the optical material used to construct the MC.