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We investigate the moderating effect of project complexity on the relationship between leadership competences of project managers and their success in projects. Building on existing studies in leadership and project management, we assess the impact of emotional (EQ), intellectual (IQ), and managerial (MQ) leadership competences on project success in different types of project complexities. A cross-sectional survey using the leadership dimensions questionnaire and project results questions yielded 119 responses, which were assessed for their type and level of complexity, measured as complexity of fact, faith, and interaction. Analysis was done through factor analysis and moderated hierarchical regression analysis. Results show that EQ and MQ are correlated with project success, but are differently moderated by complexity. The relationship between EQ and project success is moderated by complexity of faith. The relationship between MQ and project success is moderated by complexity of fact and faith. Complexity of interaction has a direct effect on project success. Analysis of variance and nonparametric tests showed the means and medians of EQ, IQ, MQ; complexities of faith, fact, and interaction do not significantly vary across different project types. This suggests using these three complexity types as a common language to research and learning across different project types.