Abstract A solitary millisecond pulsar, if near the mass limit, and undergoing a phase transition, either first or second order, provided the transition is to a substantially more compressible phase, will emit a blatantly obvious signal—spontaneous spin-up. Normally a pulsar spins down by angular momentum loss to radiation. The signal is trivial to detect and is estimated to be “on” for 1/50 of the spin-down era of millisecond pulsars. Presently about 25 solitary millisecond pulsars are known. The phenomenon is analogous to “backbending” observed in high spin nuclei in the 1970's.