  We present a detailed study of the center-of-mass (c.m.) motion seen in
simulations produced by the Simulating eXtreme Spacetimes (SXS) collaboration.
We investigate potential physical sources for the large c.m. motion in binary
black hole simulations and find that a significant fraction of the c.m. motion
cannot be explained physically, thus concluding that it is largely a gauge
effect. These large c.m. displacements cause mode mixing in the gravitational
waveform, most easily recognized as amplitude oscillations caused by the
dominant (2,$\pm$2) modes mixing into subdominant modes. This mixing does not
diminish with increasing distance from the source; it is present even in
asymptotic waveforms, regardless of the method of data extraction. We describe
the current c.m.-correction method used by the SXS collaboration, which is
based on counteracting the motion of the c.m. as measured by the trajectories
of the apparent horizons in the simulations, and investigate potential methods
to improve that correction to the waveform. We also present a complementary
method for computing an optimal c.m. correction or evaluating any other c.m.
transformation based solely on the asymptotic waveform data.
