Multi-stage, all-pass optical filters used to make low-loss, multi-channel dispersion compensation modules are disclosed. The all-pass optical filters can be ring resonators in waveguides, Gires-Tournois Interferometers (GTIs) in free space form, and the like. The coupling constants and circulating path lengths may also be distinctively varied in each of the series of GTIs, tuning the net dispersion spectrum of the GTI set, such that the sum of the dispersions from the series of GTI's can provide a system with greater bandwidth than the same number of identical GTIs. The local dispersion slope can also be tuned in this manner. Multi-cavity GTIs can also be formed with similar performance enhancing properties.