Single-fiber Bragg gratings designed to compensate for pure third-order dispersion are demonstrated. The devices are designed by use of a layer-peeling inverse-scattering technique and exhibit dispersion profiles across their reflection bandwidths of -20, +/- 40, and -225 ps/nm2 over bandwidths of 4.5, 6, and 3 nm, respectively. Furthermore, they have almost constant peak reflectivities of approximately 75% and are, respectively, only 8, 23, and 40 mm long.