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 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 a leading-order { \cal O } ( \nu ) analytically resummed radiation reaction . The EOB and the Regge-Wheeler-Zerilli 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 studies concerning the Laser Interferometer Space Antenna . We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasicircular corrections in both the gravitational wave amplitude and phase . For each multipole we tune only four next-to-quasicircular parameters by requiring compatibility between EOB and Regge-Wheeler-Zerilli waveforms at the light ring . The resulting phase difference around the merger time is as small as \pm 0.015 rad , with a fractional amplitude agreement of 2.5 \% . This suggest that next-to-quasicircular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical-relativity waveforms .