Earlier high-resolution spectroscopic studies of the fine and hyperfine structure of rovibrational levels of the 1 3delta state of NaK have been extended to include high lying rovibrational levels with v < or = 59, of which the highest levels lie within approximately 4 cm(-1) of the dissociation limit. A potential curve is determined using the inverted perturbation approximation method that reproduces these levels to an accuracy of approximately 0.026 cm(-1). For the largest values of v, the outer turning points occur near R approximately 12.7 angstroms, which is sufficiently large to permit the estimation of the C6 coefficient for this state. The fine and hyperfine structure of the 1 3delta rovibrational levels has been fit using the matrix diagonalization method that has been applied to other states of NaK, leading to values of the spin-orbit coupling constant A(v) and the Fermi contact constant b(F). New values determined for v < or = 33 are consistent with values determined by a simpler method and reported earlier. The measured fine and hyperfine structure for v in the range 44 < or = v < or = 49 exhibits anomalous behavior whose origin is believed to be the mixing between the 1 3delta and 1 1delta states. The matrix diagonalization method has been extended to treat this interaction, and the results provide an accurate representation of the complicated patterns that arise. The analysis leads to accurate values for A(v) and b(F) for all values of v < or = 49. For higher v (50 < or = v < or = 59), several rovibrational levels have been assigned, but the pattern of fine and hyperfine structure is difficult to interpret. Some of the observed features may arise from effects not included in the current model.