  We argue that the recent CLEO-c data on $e^+e^-$ annihilation into pairs of
charmed mesons at c.m. energy around 4.0 GeV are not well described by a single
resonance $\psi(4040)$, but can be better understood if there is an additional
narrow resonance with mass within few MeV from the $D^* {\bar D}^*$ threshold.
