Two modifications of the approximate analysis of interface motion during two-fluid density-driven flows of De Josselin de Jong (Proc. Euromech., 143: 75–82, 1981) are applied to the slumping of finite two-dimensional and axisymmetric brine mounds. Both lead to simple similarity solutions. One modification gives upper bounds on the time-scales of the process and the other lower bounds. The bounds are close enough to allow estimation of true behaviour within order-of-magnitude accuracy. Application of the solutions to brine-fresh interactions is illustrated by a numerical example based on natural salinas. The analysis applies to any pollutant or pollution solution denser than the groundwater, and it carries over to the converse problem of the spreading over the groundwater of a lighter pollutant (such as petroleum).