We propose the implementation of fiber Bragg gratings in tapered few-mode and multimode fibers to accomplish single-mode operation by reducing the core diameter, while preserving the core-cladding structure. The gratings present a single reflection band, and the device shows low insertion losses after the taper fabrication and the fiber Bragg gratings inscription. The excitation of high-order odd modes in the core of the fiber has been identified as the main loss mechanism; it can be prevented by means of symmetric illumination of the fibers. We also demonstrate the excitation of high-order cladding modes (cladding-air modes) along the taper transitions; these modes can be removed without a significant increment of the insertion loss.