Psychopathy research is plagued by an enigma: Psychopaths reliably act immorally, but they also accurately report whether an action is morally wrong. The current study revealed that cooperative suppressor effects and conflicting subsets of personality traits within the construct of psychopathy might help explain this conundrum. Among a sample of adult male offenders (N = 100) who ranked deserved punishment of crimes, Psychopathy Checklist-Revised (PCL-R) total scores were not linearly correlated with deserved punishment task performance. However, these null results masked significant opposing associations between task performance and factors of psychopathy: the PCL-R Interpersonal/Affective (i.e., manipulative and callous) factor was positively associated with task performance, while the PCL-R Social Deviance (i.e., impulsive and antisocial) factor was simultaneously negatively associated with task performance. These relationships were qualified by a significant interaction where the Interpersonal/Affective traits were positively associated with task performance when Social Deviance traits were high, but Social Deviance traits were negatively associated with task performance when Interpersonal/Affective traits were low. This interaction helped reveal a significant nonlinear relationship between PCL-R total scores and task performance such that individuals with very low or very high PCL-R total scores performed better than those with middle-range PCL-R total scores. These results may explain the enigma of why individuals with very high psychopathic traits, but not other groups of antisocial individuals, usually have normal moral judgment in laboratory settings, but still behave immorally, especially in contexts where Social Deviance traits have strong influence.