Complex formation between a single polyelectrolyte chain and ionic surfactant molecules is studied by computer simulation of a "primitive'' electrolyte model with explicit charges. The surfactant head carries a charge opposite to that of the polyelectrolyte. The neutral flexible tail is modeled by tethered hard spheres. A molecular bottle-brush architecture of the resulting polyelectrolyte-surfactant-complex is observed. The end-to-end distance of the polyelectrolyte is found to behave in a nonmonotonic fashion for increasing Coulomb coupling: it first gets stretched and then the stretching is reduced by self-assembling of surfactant molecules along the polyelectrolyte. The end-to-end distance of the polyelectrolyte in the complex is more pronounced for long surfactant tails. Upon addition of salt to the complex, ionic surfactant molecules condensed onto the polyelectrolyte are replaced by salt microions which leads to a weakening of the complex and to reduced end-to-end distance. (C) 2003 American Institute of Physics.