Educational versions of Millikan's oil-drop experiment have frequently been criticized; suggestions for improvement either focus on technical innovations of the setup or on replacing the experiment by other approaches of familiarization, such as computer simulations. In our approach, we have analysed experimental procedures. In doing so, we were able to identify several sources of error and took measures to minimize their influence. At the same time, we attempted to minimize the standard deviation of each individual series of measurements. Our paper describes how we developed criteria which helped to stabilize the data produced in the following series of measurements. The final series of measurements results in data which demonstrate the atomic structure of electricity and enable a demonstration of the elementary charge. (Contains 2 figures and 4 footnotes.)