A tunable dispersion compensator for the compensation of the chromatic dispersion experienced by a single-channel or multi-channel light signal. The compensator includes a plurality of optical structures such as chirped Bragg gratings or combinations thereof, each having a characteristic dispersion profile. An optical coupling arrangement successively propagates the light signal in each of these structures, so that it accumulates the dispersion compensation effect of each. A tuning device jointly tunes the dispersion profile of each optical structure by applying a same tuning force thereto, preferably a temperature gradient.