It is widely believed that advantages of hemispheric asymmetries originated in better cognitive processing, hence it is often implied that the relationship between hemispheric asymmetry and cognitive performance is linearly positive: the higher the degree of lateralization in a specific cognitive domain, the better the performance in a corresponding task. Yet, the empirical evidence for this notion is mixed and the statistical methods to analyze this relationship have been criticized. The present study therefore investigated the relationship between hemispheric asymmetries and cognitive performance in two behavioral tasks (a left-lateralized word-matching task and a right-lateralized face-decision task) in 230 participants (140 women, 90 men) by using two different approaches. Both methods correspondingly revealed that a relationship between hemispheric asymmetries and cognitive performance does exist. Contrary to a positive (linear) relationship however, the data could be best described by an inverted U-shaped curve. Although the optimal degree of lateralization seemed to be task-specific, a slight or moderate degree of hemispheric asymmetry achieved best cognitive performance in all tasks. Moreover, performances deteriorated towards extreme ends of lateralization (i.e., participants with either extreme left or right hemispheric biases). Taken together, the present study provides evidence against the notion that higher lateralization is related to enhanced cognitive performance. (Contains 2 tables and 2 figures.)