The dissolution of single bubbles of gases of low solubility kept stationary in a downward stream of water was studied. In "clean" water, two regimes are identified. Initially, the process is fast, consistent with the theory for circulating bubbles. Then, the mass-transfer rate falls sharply to that predicted for solid spheres. Transition times and transition diameters vary widely with experimental conditions. In untreated water, only the second regime is found. Results are explained in terms of the kinetics of trace surfactant accumulation at the interface. An adaptation of the stagnant-cap model is proposed, with surface immobilization expressed in terms of interface dynamics. The model yields good prediction of the transition point for a very large set of conditions, including different gases at various concentrations in the liquid stream and a wide range of initial bubble diameters.