$R$ measurement data taken with the BESII detector at center-of-mass energies between 3.7 and 5.0 GeV is fitted to determine resonance parameters (mass, total width, electron width) of the high mass charmonium states, $ψ(3770)$, $ψ(4040)$, $ψ(4160)$ and $ψ(4415)$. Various effects, including the relative phases between the resonances, interferences, the energy-dependence of the full widths, and the initial state radiative correction, are examined. The results are compared to previous studies.

9 pages, 3 figures, 1 table