  It is possible to infer the mass and spin of the remnant black hole from
binary black hole mergers by comparing the ringdown gravitational wave signal
to results from studies of perturbed Kerr spacetimes. Typically these studies
are based on the fundamental quasinormal mode of the dominant $\ell=m=2$
harmonic. By modeling the ringdown of accurate numerical relativity
simulations, we find that the fundamental mode alone is insufficient to recover
the true underlying mass and spin, unless the analysis is started very late in
the ringdown. Including higher overtones associated with this $\ell=m=2$
harmonic resolves this issue, and provides an unbiased estimate of the true
remnant parameters. Further, including overtones allows for the modeling of the
ringdown signal for all times beyond the peak strain amplitude, indicating that
the linear quasinormal regime starts much sooner than previously expected. A
model for the ringdown beginning at the peak strain amplitude can exploit the
higher signal-to-noise ratio in detectors, reducing uncertainties in the
extracted remnant quantities. Tests of the no-hair theorem should consider
incorporating overtones in the analysis.
