  We give here a new third post-Newtonisn (3PN) spin-spin contribution (in the
PN parameter $\epsilon $) to the accumulated orbital phase of a compact binary,
arising from the spin-orbit precessional motion of the spins. In the equal mass
case this contribution vanishes, but LISA sources of merging supermassive
binary black holes have typically a mass ratio of 1:10. For such non-equal
masses this 3PN correction is periodic in time, with period approximately
$\epsilon ^{-1}$ times larger than the period of gravitational waves. We derive
a renormalized and simpler expression of the spin-spin coefficient at 2PN, as
an average over the time-scale of this period of the combined 2PN and 3PN
contribution. We also find that for LISA sources the quadrupole-monopole
contribution to the phase dominates over the spin-spin contribution, while the
self-spin contribution is negligible even for the dominant spin. Finally we
define a renormalized total spin coefficient $\bar{\sigma}$ to be employed in
the search for gravitational waves emitted by LISA sources.
