BeppoSAX has detected a population of faint transient X-ray sources in the Galactic Centre. I show that a simple irradiated-disc picture gives a consistent fit to the properties of this population, and that it probably consists of low-mass X-ray binaries which have evolved beyond their minimum orbital periods 80 min. Since all post-minimum systems are transient, and neutron-star LMXBs are more common than black-hole LMXBs in the Galaxy, the majority of these systems should contain neutron stars, as observed. This picture predicts that the Galactic Centre transients should have orbital periods in the range 80 - 120 minutes, and that most of them should repeat in the next few years. In this case, the total number of post-minimum transients in the Galaxy would be considerably smaller than the usual estimates of its total LMXB population. I discuss possible reasons for this.