The production of structurally well-defined unilamellar vesicles and the control of their stability are of utmost importance for many of their applications but still a largely unresolved practical issue. In the present work we show that by admixing small amounts of amphiphilic copolymer to the original components of a spontaneously vesicle-forming surfactant mixture we are able to control the self-assembly process in a systematic way. For this purpose we employed a zwitanionic model system of zwitterionic TMDAO and anionic LiPFOS. As the copolymer reduces the line tension of the intermediately formed disks, this translates directly into a longer disk growth phase and formation of correspondingly larger vesicles. By this approach we are able to vary their size over a large range and produce vesicles of extremely low polydispersity. Furthermore, the temporal stability of the formed vesicles is enhanced by orders of magnitude in proportion to the concentration of copolymer added. This is achieved by exerting kinetic control that allows engineering the vesicle structure via a detailed knowledge of the formation pathway as obtained by highly time-resolved SAXS experiments. Synthesis of such very well-defined vesicles by the method shown should in general be applicable to catanionic or zwitanionic amphiphiles and will have far reaching consequences for controlled nanostructure formation and application of these self-assembled systems.