Control over the magnetization reversal process of nanowires is essential to current advances in modern spintronic media and magnetic data storage. Much effort has been devoted to permalloy nanostrips with rectangular cross section and vanishing crystalline anisotropy. Our aim was to unveil and control the reversal process in FeCoCu nanowires with significant anisotropy and circular cross section with tailored periodical modulations in diameter. Magneto-optical Kerr effect measurements and their angular dependence performed on individual nanowires together with their analysis allow us to conclude that the demagnetization process takes place due to the propagation of a single vortex domain wall which is eventually pinned at given modulations with slightly higher energy barrier. In addition these results create new expectations for further controlling of the propagation of single and multiple domain walls.