The work of the air-and-screen cleaner of a grain combine harvester is considered. Flows of grain–straw heap supplied for cleaning are evaluated. The methods of splitting the heap into grain and nongrain parts are described. To improve the work of the grain combine harvester cleaner, several design solutions are proposed that make possible an intensified fractionation of straw-grain heap. In the modified design of the lipped screen, the combs of the upper working sections of neighboring louver boards are offset by one half of the comb pitch. This makes it possible to improve, at an intensive heap supply, the transporting capacity of the straw particles en route to the cleaner exit. An S-type design of louver boards is proposed for a more efficient utilization of air flow in the cleaning system. These boards have a low air flow resistance and allow achieving an air flow with better aerodynamic characteristics (speed, uniformity, directionality), which makes it possible to run the combine harvester cleaning system with lower grain losses.