  We present a new, tunable effective-one-body (EOB) model of the motion and
radiation of coalescing black hole binaries with arbitrary mass ratio and
aligned spins. The most novel feature of our formalism is the introduction, and
systematic use, of the (gauge-invariant) concept of {\it centrifugal radius}
$r_{c}$. In the spinning small mass-ratio limit, the main radial potential
expressed in terms of $r_{c}$ differs very little (and only multiplicatively
so) from the usual Schwarzschild potential $1-2M/r_{c}$. This motivates a new,
multiplicative way of blending finite-mass-ratio deformations with
spin-deformations. In the present exploratory work we consider a minimal
version of our spinning EOB model (containing essentially only two adjustable
parameters: one in the Hamiltonian and one in the waveform) and calibrate its
(dominant mode) waveform against a sample of fifteen equal-mass, equal-spin
waveforms produced by the SXS collaboration, and covering the dimensionless
spin range $-0.95\leq \chi \leq +0.98$. The numerical relativity / EOB phasing
disagreement remains remarkably small ($\lesssim \pm 0.15$ rad) over the entire
spin range.
