  We derive spin-dominated waveforms (SDW) for binary systems composed of
spinning black holes with unequal masses (less than 1:30). Such systems could
be formed by an astrophysical black hole with a smaller black hole or a neutron
star companion; and typically arise for supermassive black hole encounters. SDW
characterize the last stages of the inspiral, when the larger spin dominates
over the orbital angular momentum (while the spin of the smaller companion can
be neglected). They emerge as a double expansion in the post-Newtonian
parameter $\varepsilon$ and the ratio $\xi $ of the orbital angular momentum
and dominant spin. The SDW amplitudes are presented to
($\varepsilon^{3/2},\xi$) orders, while the phase of the gravitational waves to
($\varepsilon^{2},\xi$) orders (omitting the highest order mixed terms). To
this accuracy the amplitude includes the (leading order) spin-orbit
contributions, while the phase the (leading order) spin-orbit, self-spin and
mass quadrupole-monopole contributions. While the SDW hold for any mass ratio
smaller than 1:30, lower bounds for the mass ratios are derived from the best
sensitivity frequency range expected for Advanced LIGO (giving 1:140), the
Einstein Telescope ($7\times 10^{-4}$), the LAGRANGE ($7\times 10^{-7}$) and
LISA missions ($7\times 10^{-9}$), respectively.
