Nonhuman primates constitute an indispensable model system for studying higher brain functions at the neurophysiological level. Studies involving these animals elucidated the neuronal mechanisms of various cognitive and executive functions, such as visual attention, working memory, and decision-making. Positive reinforcement training (PRT) constitutes the gold standard for training animals on the cognitive tasks employed in these studies. In the laboratory, PRT is usually based on application of a liquid reward as the reinforcer to strengthen the desired behavior and absence of the reward if the animal's response is wrong. By trial and error, the monkey may adapt its behavior and successfully reduce the number of error trials, and eventually learn even very sophisticated tasks. However, progress and success of the training strongly depend on reasonable error rates. If errors get too frequent, they may cause a drop in the animal's motivation to cooperate or its adaptation to high error rates and poor overall performance. We introduce in this report an alternative training regime to minimize errors and base the critical information for learning on graded rewarding. For every new task rule, the feedback to the animal is provided by different amounts of reward to distinguish the desired, optimal behavior from less optimal behavior. We applied this regime in different situations during training of visual attention tasks and analyzed behavioral performance and reaction times to evaluate its effectiveness. For both simple and complex behaviors, graded rewarding was found to constitute a powerful technique allowing for effective training without trade-off in accessible task difficulty or task performance. NEW & NOTEWORTHY Laboratory training of monkeys usually builds on providing a fixed amount of reward for the desired behavior, and no reward otherwise. We present a nonbinary, graded reward schedule to emphasize the positive, desired behavior and to keep errors on a moderate level. Using data from typical training situations, we demonstrate that graded rewards help to effectively guide the animal by success rather than errors and provide a powerful new tool for positive reinforcement training.