An exact closed-form synthesis method is proposed for the design of narrowband reflection-type (mono-port) phasers with arbitrary prescribed group-delay responses. The proposed synthesis technique consists in three steps. First, it transforms the phase problem from the bandpass domain to the low-pass domain using a one-port ladder network, where a mathematical synthesis is performed via a Hurwitz polynomial. Second, it transforms the synthesized low-pass network back to the bandpass domain for implementation in a specific technology. Third, it uses an iterative post-distortion correction technique to compensate for distributed effects over the broader bandwidth required. The proposed synthesis method is verified by both full-wave analysis and experiment where the synthesized bandpass network is realized in an iris-coupled waveguide configuration.