Recent experimental studies have shown that buoyancy-thermocapillary convection in a layer of volatile liquid subjected to a horizontal temperature gradient is strongly affected by the presence of noncondensable gases, such as air. Specifically, it was found that removing most of the air from a sealed cavity containing the liquid and its vapors significantly alters the flow structure and, in particular, suppresses transitions between the different convection patterns found at atmospheric conditions. Yet, at the same time, the concentration of noncondensables has almost no effect on the flow speeds in the liquid layer, at least for the parameter range studied in the experiments. To understand these results, we have formulated and numerically implemented a detailed model that accounts for mass and heat transport in both phases as well as the phase change at the interface. The predictions of this model, which assumes that the gas phase is dominated by either noncondensables or the vapor, agree well with experiments in both limits. Furthermore, we find that noncondensables have a large effect on the flow at concentrations even as low as 1%, i.e., values much lower than those achieved in experiment. (C) 2015 Elsevier Ltd. All rights reserved.