  We introduce a new, resummed, analytical form of the post-Newtonian (PN),
factorized, multipolar amplitude corrections $f_{\ell m}$ of the
effective-one-body (EOB) gravitational waveform of spinning, nonprecessing,
circularized, coalescing black hole binaries (BBHs). This stems from the
following two-step paradigm: (i) the factorization of the orbital
(spin-independent) terms in $f_{\ell m}$; (ii) the resummation of the residual
spin (or orbital) factors. We find that resumming the residual spin factor by
taking its inverse resummed (iResum) is an efficient way to obtain amplitudes
that are more accurate in the strong-field, fast-velocity regime. The
performance of the method is illustrated on the $\ell=2$ and $m=(1,2)$ waveform
multipoles, both for a test-mass orbiting around a Kerr black hole and for
comparable-mass BBHs. In the first case, the iResum $f_{\ell m}$'s are much
closer to the corresponding "exact" functions (obtained solving numerically the
Teukolsky equation) up to the light-ring, than the nonresummed ones, especially
when the black-hole spin is nearly extremal. The iResum paradigm is also more
efficient than including higher post-Newtonian terms (up to 20PN order): the
resummed 5PN information yields per se a rather good numerical/analytical
agreement at the last-stable-orbit, and a well-controlled behavior up to the
light-ring. For comparable mass binaries (including the highest PN-order
information available, 3.5PN), comparing EOB with Numerical Relativity (NR)
data shows that the analytical/numerical fractional disagreement at merger,
without NR-calibration of the EOB waveform, is generically reduced by iResum,
from a $40\%$ of the usual approach to just a few percents. This suggests that
EOBNR waveform models for coalescing BBHs may be improved using iResum
amplitudes.
