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When we grasp an object, our visuomotor system has to solve an intricate problem: how to find the best out of an infinity of possible contact points of the fingers with the object? The contact point selection model (CoPS) we present here solves this problem and predicts human grasp point selection in precision grip grasping by combining a few ... basic rules that have been identified in human and robotic grasping. Usually, not all of the rules can be perfectly satisfied. Therefore, we assessed their relative importance by creating simple stimuli that put them into conflict with each other in pairs. Based on these conflict experiments we made model-based grasp point predictions for another experiment with a novel set of complexly shaped objects. The results show that our model predicts the human choice of grasp points very well, and that observers´ preferences for their natural grasp angles is as important as physical stability constraints. Incorporating a human grasp point selection model like the one presented here could markedly improve current approaches to cortically guided arm and hand prostheses by making movements more natural while also allowing for a more efficient use of the available information.