The angular dependence of longitudinal Na-23 NMR spin relaxation in a lyotropic calamitic nematic phase is determined using a simple rotor technique. Analyzing the director-frame spectral densities, J(n)(D)(omega), n = 0, 1, 2, and the quadrupole splitting shows that the experimental data cannot be accounted for in terms of the prolate micellar aggregates being uniaxial. Rather, the results indicate the micelles to be biaxial, with approximate axial ratios of rho(-) approximate to 1.5 and rho(+) approximate to 3-5. Comparison with previous investigations of the nematic region in the sodium dodecyl sulfate-decanol-water system shows the interfacial curvature of the micelles to vary with composition in a way similar to that observed in the lamellar phase.