This paper tackles the project scheduling problem in presence of complex networks of activities, resource constraints, overlapping and rework. The objective is to analyse the influence of project characteristics, such as project size, resource constraints, overlapping opportunities and rework, on the efficiency of overlapping in terms of reduction of the project makespan. An exact solution procedure and a metaheuristic are thus proposed to minimize the project makespan, while limiting the use of overlapping. A two-part model is used to conduct a statistical analysis of the influence of project characteristics on the makespan gain with overlapping. Results suggest that the best overlapping decision should consist in overlapping few pairs of overlappable activities with a large degree of overlapping. Furthermore, for complex projects, overlapping decisions should not rely solely on the criticality of the activities. These findings provide a better understanding of overlapping decisions and should guide planners in improving existing practices.