Significance One critical challenge of solar thermal distillation is the need to collect and focus sunlight, since purified water output increases with increasing solar intensity. Here we show substantial increases in the efficiency of solar thermal distillation by redistributing direct sunlight intensity with small focusing elements rather than by increasing overall intensity with large solar concentrators. This is because solar thermal distillation depends upon the saturation vapor pressure of water, which has an exponential temperature dependence, making purified water output exponentially dependent upon light intensity. This observation should redirect design efforts to focus on exploiting this nonlinearity, rather than increasing solar collector size, for higher-performance solar water purification systems within a small footprint, suitable for portability and use in remote locations.