Polymer-surfactant mixtures are found in many industrial formulations, and hence there is a significant interest in understanding, at a molecular level, how the self-assembly of surfactant is affected by oppositely-charged polyelectrolytes (PEs). We use self-consistent field modeling and show that the modes of interaction of PEs strongly depend on the architecture of the PE on the segmental level. Hydrophilic cationic PEs with their charge proximal to the linear backbone are expected to bind electrostatically to the outsides of the coronas of the spherical micelles of anionic surfactants, such as sodium laureth sulphate (SLES). As a result, the surfactant aggregation number increases, but at the same time the colloidal stability deteriorates, due to bridging of the PEs between micelles. PEs with their charge somewhat displaced from the backbone by way of short hydrophobic spacers, are expected to be present inside a micelle at the core-corona boundary. In this case the aggregation number decreases, yet the colloidal stability is retained. Hence, SLES tends to remove hydrophilic PEs from an aqueous solution, whereas it solubilizes more hydrophobic ones. The binding isotherm shows that the uptake of PEs remains typically below charge compensation and in this case the spherical micelle topology remains the preferred state.