Vertical distributions of Δ18O were used to constrain hydraulic conductivity (K) in a thick, unfractured aquitard. Previous investigations utilizing permeability tests at a variety of scales <Keller et al., 1989> indicated that bulk K at the site ranges from 3.5¿10-11 m/s to 1.2¿10-10 m/s. Advective displacements calculated on the basis of these K values lead to a wide range of predicted distributions of natural tracers after 11,000 years. Comparison of Δ18O distributions and simulated advection-diffusion profiles provide a more precise constraint on advective displacement and hence on K. The simulations, cast in terms of a Peclet number (P=V2T/D*) ranging in value from 0 to 12, indicate that transport is diffusion controlled and that K is actually less than 1.2¿10-11 m/s. P greater than 0.1 (K>1.2¿10-11 m/s) overestimates transport. This result indicates that conventional permeability tests in very tight media tend to overestimate K. In practical terms, advective transport at the site is negligible, and transport can be simulated with diffusion only (P=0). ¿ American Geophysical Union 1996