We study the evolution of the magnetoresistance (MR) in Permalloy nanocontacts prepared by controlled low-temperature UHV electromigration in nanoring segment structures with constrictions. The ring geometry allows for the controlled and reproducible positioning of a domain wall in the nanocontacts. We observe three different resistance levels, corresponding to distinct domain-wall positions. A change in the sign of the MR difference, between a domain wall at the constriction and a domain wall next to the constriction, occurs with decreasing constriction width. This is in line with our micromagnetic simulations, where the MR is calculated based on the anisotropic MR (AMR) effect.