The azimuthal dependence of third-order and cascaded second-order nonlinear coupling was used to measure the relative contributions of each to direct third-harmonic generation in beta-barium borate. This permitted the measurement of the values of tensor elements chi(3)(10) , chi(3)(11) , and chi(3)(16) relative to the known chi(2)(ij) . Finally, conversion efficiencies to 3 omega of up to 6% were achieved with a femtosecond chirped-pulse amplification laser with 200 GW/cm(2) in collimated beams.