Centrosomes organize microtubule structures in animal cells. The centrosome duplicates once per cell cycle in most dividing cells via a pathway that relies on a pre-existing centrosome. The molecular mechanism of this 'once and only once' control is not understood, and recent results show that centrosomes can also be assembled by a de novo pathway that bypasses this control. These results require a rethinking of how proper centrosome number is maintained. We propose that the engagement of centrioles with each other normally blocks centrosome re-duplication, and that disengagement of centrioles from each other at the end of mitosis licenses them for duplication in the subsequent cell cycle.