Tidal capture products dominate the population of active binaries in globular clusters. Recycled radio pulsars will provide the first extensive sample of the period distribution of such binaries. The expected orbital period distribution is computed for the standard evolutionary scenarios involving mass transfer in binaries with captured stars near the present turn-off mass; comparison with the observed distribution suggests that this evolutionary picture requires significant modification. In agreement with studies of the population of recycled cluster pulsars, the orbital periods of the observed binaries indicate that these modifications should substantially shorten the mass transfer phases during which the pulsar progenitor is a bright X-ray source. 43 refs.