Purpose Constructive deviance is a behavior that can contribute to the effectiveness of an organization despite its problematic nature. Too few studies have examined the correlates of this behavior. The purpose of this study is to examine variables that represent exchange and organizational culture and their relationship to supervisor-reported and self-reported constructive deviance. Design/methodology/approach The survey data were collected from 602 employees (a response rate of 67 per cent) in a large municipality in central Israel. Hierarchical linear modeling (HLM) analyses were performed for each of the dependent variables (three self-reported constructive deviances and three supervisor-reported constructive deviance) controlling for divisions and departments. Findings The findings showed that self-reported constructive deviance was explained much better by the independent variables than supervisor-reported deviance. Organizational justice and moral identity had a strong direct effect on constructive deviance (self-reported). The mediation effect showed that an organizational climate for innovation had the strongest mediation effect among the mediators. Psychological contract breach was found to have a limited effect on constructive deviance. Practical implications Organizations should encourage procedural justice to encourage their employees to act in support of the organization, whether openly (formal performance) or more secretly (constructive deviance). Also, organizations should support innovation climate if they want to increase constructive deviance of their employees. Originality/value In a time when innovation and creativity are gaining increasing importance as behaviors that contribute to organizational success, more research on constructive deviance is expected. This study increases our understanding of this important concept stimulates additional studies of it.