Manipulation is the most exciting feature of the non-contact atomic force microscopy technique as it allows building nanostructures on surfaces. Usually vertical manipulations are accompanied by an abrupt tip modification leading to a change of contrast. Here we report on low-temperature experiments demonstrating vertical manipulations of 'super'-Cu atoms on the p(2 × 1) Cu(110):O surface, both extractions to and depositions from the tip, when the imaging contrast remains the same. These results are rationalized employing a novel and completely general method that combines density functional theory calculations for obtaining energy barriers as a function of tip height and a Kinetic Monte Carlo algorithm for studying the tip dynamics and extraction of manipulation statistics. The model reveals a novel multi-step manipulation mechanism combining activated jumps of 'super'-Cu atoms to/from the tip with their drag by and diffusion on the tip.