  We have performed an analysis of the $e^+ e^- \to D^{(*)} \bar D^{(*)}$ data
in the region of the $\psi(4040)$ and $\psi(4160)$ resonances which have a
substantial overlap and require special care. By using the $^3 P_0$ model to
relate the different $D^{(*)} \bar D^{(*)}$ production modes, we make
predictions for production of these channels and compare with experiment and
other theoretical approaches. As a side effect we find that these resonances
qualify largely as $c \bar c$ states and the weight of the meson-meson
components in the wave function is very small.
