We investigate from a practitioner's point of view the computation of the ionization potential (IP) within density-functional theory (DFT). DFT with (semi)local energy-density functionals is plagued by a self-interaction error which hampers the computation of the IP from the single-particle energy of the highest occupied molecular orbital (HOMO). The problem may be cured by a self-interaction correction (SIC) for which there exist various approximate treatments. We compare the performance of the SIC proposed by Perdew and Zunger with the very simple average-density SIC (ADSIC) for a large variety of atoms and molecules up to larger systems such as carbon rings and chains. Both approaches to the SIC provide a large improvement to the quality of the IP if calculated from the HOMO level. The surprising result is that the simple ADSIC performs even better than the original Perdew-Zunger SIC in the majority of the studied cases.