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Harvesting of high-moisture corn ears poses a challenge due to the high level of grain damage. In the present study, a series of concaves adapted to moist corn ears threshing was developed and evaluated. The key improvements include a concave arc shape and oblique crossbars to reduce corn grain damage and threshing losses. Results show that the geometrical shape of the concave arc and its crossbars have a significant influence on the grain detachment from the ears, grain separation through the concave, and grain damage during the threshing process of moist ears of corn. Studies show that replacing the concave rounded crossbars with oblique ones can increase threshing performance of moist corn ears. A concave with an Archimedes’ spiral arc and oblique concave crossbars is an effective approach to improve corn grain quality and reduce harvest losses due to grain damage. We identify the optimal design for threshing corn ears as an experimental concave with an Archimedes’ spiral arc of 8 mm height, with 19 mm wide crossbars of the concave with an oblique working plane (tilt angle 25°). This design achieves minimal threshing grain losses (0.03%) when threshing moist ears (grain moisture content ~35%), and damaged grain in the threshing apparatus does not exceed the permissible limit of 3% at an ear feed rate of 16.8 kg s−1.