This paper presents results for the efficiency of a stratified chilled-water storage tank with one inlet and one outlet. Numerical solutions for the two-dimensional, unsteady, laminar flow during stably stratified tank filling are compared with a one-dimensional model involving only conductive heat transfer across the thermocline separating the entering cold water and the exiting warm water. This one-dimensional model represents the minimum level of thermal mixing. The difference between the one-dimensional and two-dimensional models are revealed by a horizontal average of the governing equation for the two-dimensional model. Comparison reveals that for inlet Reynolds numbers of approximately 100, the efficiency of the actual, two-dimensional filling is less than 10% below the optimal efficiency of the model. Examination of an effective diffusivity, which can be associated with the mixing ignored in the one-dimensional model, reveals that the early and late stages of the tank-filling process are responsible for most of the deviation between the actual and ideal performances. For the present Reynolds number range, the two-dimensional predictions for effective diffusivity agree well with values derived from published experimental data.