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Interference phenomena observed in the $\psi(3770)$ resonance region in thereactions $e^+e^-$ $\to$ $ D\bar D$ are analyzed. To avoid ambiguities in thedetermination of the $\psi(3770)$ resonance parameters, when analyzing databetween the $D\bar D$ and $D\bar D\pi$ thresholds, the amplitudes satisfyingthe elastic unitarity requirement should be used. In the lack of information onthe $P$ wave of $D\bar D$ elastic scattering, the $\psi(3770)$ parameters,determined by fitting the $e^+e^-$ $\to $ $D\bar D$ data, can essentiallydepend on the model used for the total contribution of the resonance andbackground. The selection of the models can be toughened by comparing theirpredictions with the relevant data on the shape of the $\psi(3770)$ peak in thenon-$D\bar D$ channels $e^+e^-$ $\to $ $\gamma\chi_{c0}$, $J/\psi\eta$,$\phi\eta$, etc.

Line shape of \psi(3770) in e^+e^-\to D\bar D