  We investigate the effect of resonance decays on the three-particle
correlator charge separation observable in search for the chiral magnetic
effect, using a simple simulation with realistic inputs. We find that resonance
decays can largely account for the measured signal. We suppress the elliptic
flow ($v_2$) background by using zero event-by-event $v_2$ (or via the
mixed-event technique). We find that the background is suppressed, but not
eliminated as naively anticipated. We identify the reason to be the
non-identicalness of the resonance and final-state particle's $v_2$ and the
induced correlation between the transverse momentum dependent resonance $v_2$
and decay angle. We make predictions for the charge separation signal due to
resonance decays in 200~GeV Au+Au collisions.
