  We discuss the properties of the effective-one-body (EOB) multipolar
gravitational waveform emitted by nonspinning black-hole binaries of masses
$\mu$ and $M$ in the extreme-mass-ratio limit, $\mu/M=\nu\ll 1$. We focus on
the transition from quasicircular inspiral to plunge, merger and ringdown.We
compare the EOB waveform to a Regge-Wheeler-Zerilli (RWZ) waveform computed
using the hyperboloidal layer method and extracted at null infinity. Because
the EOB waveform keeps track analytically of most phase differences in the
early inspiral, we do not allow for any arbitrary time or phase shift between
the waveforms. The dynamics of the particle, common to both wave-generation
formalisms, is driven by leading-order ${\cal O}(\nu)$ analytically--resummed
radiation reaction. The EOB and the RWZ waveforms have an initial dephasing of
about $5\times 10^{-4}$ rad and maintain then a remarkably accurate phase
coherence during the long inspiral ($\sim 33$ orbits), accumulating only about
$-2\times 10^{-3}$ rad until the last stable orbit, i.e. $\Delta\phi/\phi\sim
-5.95\times 10^{-6}$. We obtain such accuracy without calibrating the
analytically-resummed EOB waveform to numerical data, which indicates the
aptitude of the EOB waveform for LISA-oriented studies. We then improve the
behavior of the EOB waveform around merger by introducing and tuning
next-to-quasi-circular corrections both in the gravitational wave amplitude and
phase. For each multipole we tune only four next-to-quasi-circular parameters
by requiring compatibility between EOB and RWZ waveforms at the light-ring. The
resulting phase difference around merger time is as small as $\pm 0.015$ rad,
with a fractional amplitude agreement of 2.5%. This suggest that
next-to-quasi-circular corrections to the phase can be a useful ingredient in
comparisons between EOB and numerical relativity waveforms.
