The hexagonal (E) liquid-crystalline phase in mixtures of sodium desoxycholate (NaDOC) with the cationic surfactant cetyltrimethylammonium bromide (CTAB) in water has been investigated by small-angle X-ray diffraction and optical polarizing microscopy. Large proportions of the dihydroxy bile salt can be incorporated in the E phase of the detergent and lead to a decreasing average radius from 22 Angstrom for pure CTAB to 19.5 Angstrom at 46 mole% of NaDOC, The introduction of the bile salt in the cylinders thus increases the curvature, whereas the same bile salt induces a transition to rod-like micelles when added to spherical CTAB micelles at low surfactant concentration. The mixed E phase was identified and characterized as a hexagonal mesophase by optical polarizing microscopy. The diffusion-limited fluorescence quenching of excited state pyrene by dimethylbenzophenone was investigated in the cylindrical mixed micelles of the micellar (L(1)) phase in the same system. The decay curves were evaluated using a model of excited state deactivation in infinitely long rod-like micelles without exchange of quenchers (Almgren, M., Alsins, J., Mukhtar, E., and van Stam, J., J, Phys. Chen, 92, 4479 (1988)) and gave as results the relative diffusion coefficient of the excited probe and quencher, The addition of DOC- up to an equimolar concentration decreased the diffusion coefficient substantially, indicating an increased rigidity of the micelle.