Some of the global warming from anthropogenic greenhouse gases is offset by increased reflection of solar radiation by clouds with smaller droplets that form in air polluted with aerosol particles that serve as cloud condensation nuclei. The resulting cooling tendency, termed the indirect aerosol forcing, is thought to be comparable in magnitude to the forcing by anthropogenic CO2, but it is difficult to estimate because the physical processes that determine global aerosol and cloud populations are poorly understood. Smaller cloud droplets not only reflect sunlight more effectively, but also inhibit precipitation, which is expected to result in increased cloud water. Such an increase in cloud water would result in even more reflective clouds, further increasing the indirect forcing. Marine boundary-layer clouds polluted by aerosol particles, however, are not generally observed to hold more water. Here we simulate stratocumulus clouds with a fluid dynamics model that includes detailed treatments of cloud microphysics and radiative transfer. Our simulations show that the response of cloud water to suppression of precipitation from increased droplet concentrations is determined by a competition between moistening from decreased surface precipitation and drying from increased entrainment of overlying air. Only when the overlying air is humid or droplet concentrations are very low does sufficient precipitation reach the surface to allow cloud water to increase with droplet concentrations. Otherwise, the response of cloud water to aerosol-induced suppression of precipitation is dominated by enhanced entrainment of overlying dry air. In this scenario, cloud water is reduced as droplet concentrations increase, which diminishes the indirect climate forcing.