The hyperfine structures of the 2 (3)Sigma(g)(+), 3 (3)Sigma(g)(+), and 4 (3)Sigma(g)(+) states of Na-2 have been resolved with sub-Doppler continuous wave perturbation facilitated optical-optical double resonance spectroscopy via A (1)Sigma(u)(+)similar tob (3)Pi(u) mixed intermediate levels. The hyperfine patterns of these three states are similar. The hyperfine splittings of the low rotational levels are all very close to the case b(betaS) limit. As the rotational quantum number increases, the hyperfine splittings become more complicated and the coupling cases become intermediate between cases b(betaS) and b(betaJ) due to spin-rotation interaction. We present a detailed analysis of the hyperfine structures of these three (3)Sigma(g)(+) states, employing both case b(betaS) and b(betaJ) coupling basis sets. The results show that the hyperfine splittings of the (3)Sigma(g)(+) states are mainly due to the Fermi-contact interaction. The Fermi contact constants for the two dsigma Rydberg states, the 2 (3)Sigma(g)(+) and 4 (3)Sigma(g)(+), are 245+/-5 MHz and 225+/-5 MHz, respectively, while the Fermi contact constant of the ssigma 3 (3)Sigma(g)(+) Rydberg state is 210+/-5 MHz. The diagonal spin-spin and spin-rotation constants, and nuclear spin-electronic spin dipolar interaction parameters of the 3 (3)Sigma(g)(+) and 4 (3)Sigma(g)(+) states are also obtained. (C) 2004 American Institute of Physics.