From a critical evaluation of the relevant literature Harned coefficients at 25 degrees C and their corresponding trace activity coefficients are reported for 72 mixtures of strong aqueous electrolytes with a common ion. The work confirms the generality of Harned's rule in its simplest form, that is, with only one (linear) term. Uncertainties in predicted mean activity coefficients are typically less than 0.01, comparable with the experimental reproducibility. Unless there are good grounds to suggest that significant changes in chemical speciation are occurring, experimental measurements that do not conform to the rule should be regarded with suspicion. We find that the estimates of errors made by authors of single potentiometric investigations are often as much as an order of magnitude too optimistic. Even the work of Harped and colleagues, which was typically of high quality, is sometimes much worse than is claimed or implied in the literature. The unfortunately common practice of introducing a quadratic term (as a second adjustable parameter) to extend Harned's rule is unjustified, within the true current limits of experimental error. Harned's rule with just one coefficient provides a description of aqueous strong electrolyte mixing thermodynamics which is widely applicable, satisfactorily accurate, and without sign of any systematic problem.