A new algorithm is developed to solve models with heterogeneous agents and aggregate uncertainty. Projection methods are the main building blocks of the algorithm and – in contrast to the most popular solution procedure – simulations only play a very minor role. The paper also develops a new simulation procedure that not only avoids cross-sectional sampling variation but is 10 (66) times faster than simulating an economy with 10,000 (100,000) agents. Because it avoids cross-sectional sampling variation, it can generate an accurate representation of the whole cross-sectional distribution. Finally, the paper outlines a set of accuracy tests.