  We investigate the detectability of sub-dominant spin effects in merging
black-hole binaries using current gravitational-wave data. Using a
phenomenological model that separates the spin dynamics into precession
(azimuthal motion) and nutation (polar motion), we present constraints on the
resulting amplitudes and frequencies. We also explore current constraints on
the spin morphologies, indicating if binaries are trapped near spin-orbit
resonances. We dissect such weak effects from the signals using a sequential
prior conditioning approach, where parameters are progressively re-sampled from
their posterior distribution. This allows us to investigate whether the data
contain additional information beyond what is already provided by quantities
that are better measured, namely the masses and the effective spin. For the
current catalog of events, we find no significant measurements of weak spin
effects such as nutation and spin-orbit locking. We synthesize a source with a
high nutational amplitude and show that near-future detections will allow us to
place powerful constraints, hinting that we may be at the cusp of detecting
spin nutations in gravitational-wave data.
