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The existence of millisecond pulsars with planet-mass companions (Bailes etal., 2011) in close orbits is challenging from the stellar evolution point ofview. We calculate in detail the evolution of binary systems self-consistently,including mass transfer, evaporation and irradiation of the donor by X-raysfeedback, demonstrating the existence of a new evolutionary path leading toshort periods and compact donors as required by the observations of PSRJ1719-1438. We also point out the alternative of an exotic nature of thecompanion planet-mass star.

Evolutionary trajectories of ultra-compact "black widow" pulsars with very low mass companions