The resonance parameters of the excited psi-family resonances, namely the psi(4040), psi(4160), and psi(4415), were determined by fitting the R-values measured by experiments. It is found that the previously reported leptonic partial widths of these
states were merely one possible solutions among a four-fold ambiguity. By fitting the most precise experimental data on the R-values measured by the BES collaboration, this work presents all four sets of solutions. These results may affect the interpretation of the charmonium and charmonium-like states above 4GeV/c^2.
