High-resolution x-ray scattering experiments to study the critical smectic-A fluctuations in the nematic phase have been performed on a mixture of two nonpolar, two-benzene-ring compounds. The ratio T(NA)/T(NI) (= 0.885) for this mixture is much smaller than for previously studied similar materials. The smectic correlation lengths parallel and perpendicular to the smectic-layer normal are found to diverge anisotropically with characteristic exponents-nu parallel-to = 0.75 +/- 0.03, nu perpendicular-to = 0.65 +/- 0.03, and the susceptibility with gamma = 1.24 +/- 0.05.