The local structure and composition of the diamond paramagnetic defects labelled N3 and OK1 in which two heteroatoms (one of them is nitrogen) occupy vicinal substitutional positions are still a matter of debate. The electron paramagnetic resonance (EPR) is the technique adopted experimentally to characterize these defects, whose ground state is a doublet. In the present study, two models suggested in literature that contain N and 0 impurities are investigated at the quantum mechanical level by using the supercell model, a local Gaussian-type basis set, and the hybrid B3LYP functional as implemented in the CRYSTAL code. The computed EPR results (the Fermi contact and the available elements of the hyperfine coupling and electric field gradient tensors) are in good agreement (much better than in all previous, in some cases recently, studies) with an experiment. The two defects are further characterized in terms of local geometry, charge and spin density distributions, and IR and Raman spectra.