  We demonstrate that the dip observed near the total energy of 3872 MeV in the
recent cross section data from the BESIII Collaboration for $e^+e^-\to
J/\psi\pi^+\pi^- $ admits a natural explanation as a coupled-channel effect: it
is a consequence of unitarity and a strong $S$-wave $D\bar D^*$ attraction that
generates the state $X(3872)$. We anticipate the appearance of a similar dip in
the $e^+e^-\to J/\psi\pi^+\pi^-\pi^0$ final state near the $D^*\bar{D}^*$
threshold driven by the same general mechanism, then to be interpreted as a
signature of the predicted spin-two partner of the $X(3872)$.
