We report the observation of an intermediate mesh phase with rhombohedral symmetry, corresponding to the space group R $$($) over barm, in a mixed surfactant system formed by the cationic surfactant cetyltrimethylammonium bromide (CTAB) and the organic salt 3-sodium-2-hydroxy naphthoate (SHN). It occurs between a random mesh phase L-alpha(D) phase transforms continuously into the L-alpha phase with an increasing surfactant concentration (phi(s)). To separate the effects of salt and phi(s) on the phase behavior, the ternary system consisting of cetyltrimethylammonium 3-hydroxy-naphthalene-2-carboxylate (CTAHN), sodium bromide (NaBr), and water was studied. The intermediate mesh phase is found in this system at high NaBr concentrations. The micellar aggregates, both in the intermediate and random mesh phases, are found to be made up of a two-dimensional network of rod-like segments, with three rods meeting at each node. The average mesh size increases with phi(s), and the transition from the random mesh phase to the intermediate phase is found to occur when it is approximately 1.5 times the lamellar periodicity. The intermediate mesh phase is absent in the equimolar dodecyltrimethylammonium bromide (DTAB)-SHN system, indicating the role of the surfactant chain length in the formation of this phase. This system exhibits a random mesh phase over a very wide range of water content, with the average mesh size decreasing upon an increasing phi(s), contrary to the trend seen in the CTAB-SHN system.