Aerosols have a potentially large effect on climate, particularly through their interactions with clouds, but the magnitude of this effect is highly uncertain. Large volcanic eruptions produce sulfur dioxide, which in turn produces aerosols; these eruptions thus represent a natural experiment through which to quantify aerosol–cloud interactions. Here we show that the massive 2014–2015 fissure eruption in Holuhraun, Iceland, reduced the size of liquid cloud droplets—consistent with expectations—but had no discernible effect on other cloud properties. The reduction in droplet size led to cloud brightening and global-mean radiative forcing of around −0.2 watts per square metre for September to October 2014. Changes in cloud amount or cloud liquid water path, however, were undetectable, indicating that these indirect effects, and cloud systems in general, are well buffered against aerosol changes. This result will reduce uncertainties in future climate projections, because we are now able to reject results from climate models with an excessive liquid-water-path response.