The complexation between a charged micelle and an oppositely charged polyelectrolyte was studied by using a simple model system with a particular emphasis on the electrostatic interaction and the polyelectrolyte rigidity. Structural data of the micelle-polyelectrolyte complex and thermodynamic quantities of the complexation as a function of the flexibility of the polyelectrolyte were obtained by using Monte Carlo simulation and thermodynamic integration. Moreover, the ratio of the critical aggregation concentration, cac, and the critical micellization concentration, cmc, was calculated, cac being the lowest surfactant concentration at which the surfactants self-aggregate in the presence of polyelectrolyte. The cac was found to be ca. 4 (rigid polyelectrolyte) to ca. 60 (flexible polyelectrolyte) times lower than the cmc. The latter value is in line with experimental data of similar systems. Hence, it seems that the electrostatic interactions as well as the rigidity of the polyelectrolyte are important factors for controlling the reduction of the cmc.