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Lossless all-pass optical filters are introduced, which can approximate any desired phase response while maintaining a constant, unity amplitude response. Architectures using cascade and lattice structures based on ring resonators and cavities defined by reflectors are discussed. Two applications are presented: 1) for fiber dispersion compensation and 2) for compensation of the nonlinear phase response of narrow bandpass optical filters such as thin-film or Bragg grating filters. All orders of dispersion can be compensated in principle, and the filters are periodic so multiple channels can be compensated with a single device. The architectures are very compact compared to alternatives such as chirped Bragg gratings.