Atomistic modeling of segregation in Ni-Ti alloys is performed using the Bozzolo-Ferrante-Smith (BFS) method for alloys. It is found that Ti segregation to the surface decreases rapidly even for small increases in Ni concentration. A competing process is identified in the vicinity of surface defects, leading to excess Ti coverage of the exposed surface and the creation of Ti-covered pits. A simple explanation based on an atom-by-atom energy analysis is found to satisfactorily explain the observed effects.