Using the effective potential methods that we presented in a previous Letter (see this longer Physical Review D paper for details), we recently discovered that certain black hole binary configurations where the spins are aligned with the orbital angular momentum are unstable, and they can start precessing during their evolution. This can have observational implications in the electromagnetic and gravitational radiation emitted by these systems. Our paper on the precessional instability appeared in Physical Review Letters today, and it was selected as an Editors’ Suggestion.