By regarding adsorbed and dissolved surfactant as independent species whose chemical potentials are equal at equilibrium, general expressions are derived which specify the conditions for the Gibbs surface excess of surfactant, Γ, and the contribution from an adsorbed monolayer, Γm, to exhibit maxima with increasing surfactant concentration. These conditions do not appear to be thermodynamically or otherwise forbidden and lead to the conclusion that situations may arise in which the total number density of solute in an interfacial region decreases with increasing bulk concentration. An example based on a simplified model is used to show that the appropriate conditions might be fulfilled in practice by some micellar solutions of ionic surfactants. Similar reasoning could also apply to surfactant binding on polymers.