EPR spectra for copper doped single crystals of LiNbO have been studied at temperatures from 1.3K to 133K. Copper, a 3d ion configuration, substitutes for one of the cations (site symmetry of C3) as Cu+. As a result of coupling to lattice vibrations, the ground manifold consists of a doubly degenerate vibronic ground state and a nearby singlet. An affective Hamiltonian that Includes the strain, Zeeman, and hyperflne interactions is formulated for ground manifolds of* l) doubly degenerate ground state, 2) doubly degenerate ground state with a singlet nearby, and 3) an accidentally degenerate triplet composed of a doublet and singlet. Further, an effective Hamiltonian (call it Hamiltonian number 4) for defect association is also formulated. The eigenvalue problems for these four effective Hamiltonians are solved using perturbation techniques and their predictions are compared to the EPR spectra. Because of the observed line intensities the spectra appears to fit most closely case 2), the so-called intermediate JahnTeller effect. High frequency EPR spectra must be obtained before Hamiltonians 3) and 4) can be entirely rulled out. Particular attention is given to the theoretical predictions of Hamiltonian 1) (the dynamic Jahn-Teller effective Hamiltonian) in which new spectral possibilities are presented. These new anisotropy features are shown to be a generalization of previous analyses.