A systematic study of the impact of annealing on the electronic properties of single InAs/GaAs quantum dots (QDs) is presented. Single QD cathodoluminescence spectra are recorded to trace the evolution of one and the same QD over several steps of annealing. A substantial reduction of the excitonic fine-structure splitting upon annealing is observed. In addition, the binding energies of different excitonic complexes change dramatically. The results are compared to model calculations within 8-band k·p theory and the configuration interaction method, suggesting a change of electron and hole wave function shape and relative position.