  The masses of $\psi((n+1) {}^3S_1)$ and $\psi(n {}^3D_1)$ are calculated
using the relativistic string Hamiltonian with "linear+gluon-exchange"
potential. They occur in the range 4.5-5.8 GeV, in particular, $M(3D)=4.54$
GeV, $M(5S)=4.79$ GeV, $M(4D)=4.85$ GeV are calculated with accuracy $\sim 50$
MeV. Linear Regge trajectories: $M^2(nS)=M^2(\psi(4.42))+ 2.91$ GeV$^2 (n-4)$
$(n\geq 4) $ and $M^2(nD)=(4.54^2+ 2.88 (n-3))$ GeV$^2$ ($n\geq 3$) are
obtained only for higher charmonium excitations. They have slopes two times
larger than those of light mesons and give good description of calculated
masses. These masses are compared with enhancements in some recent $e^+e^-$
experiments.
