  We establish the set of independent variables suitable to monitor the
complicated evolution of the spinning compact binary during the inspiral. Our
approach is valid up to the second post-Newtonian order, including leading
order spin-orbit, spin-spin and mass quadrupol-mass monopole effects, for
generic (noncircular, nonspherical) orbits. Then we analyze the conservative
spin dynamics in terms of these variables. We prove that the only binary black
hole configuration allowing for spin precessions with equal angular velocities
about a common intantaneous axis roughly aligned to the normal of the
osculating orbit, is the equal mass and parallel (aligned or antialigned) spin
configuration. This analytic result puts limitations on what particular
configurations can be selected in numerical investigations of compact binary
evolutions, even in those including only the last orbits of the inspiral.
