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−→J/ψπ+π− admits a natural explanation as a coupled-channel effect: it is a consequence of unitarity and a strong S-wave DD¯* attraction that generates the state X(3872). We anticipate the appearance of a similar dip in the e+e−→J/ψπ+π−π0 final state near the D*D¯* threshold driven by the same general mechanism, then to be interpreted as a signature of the predicted spin-2 partner of the X(3872). Published by the American Physical Society 2024