Two different issues, important for the pumping mechanism of cyctochrome c oxidase, have been addressed in the present study. One of them concerns the nature of two key proton transfer transition states. A simple electrostatic model is used to suggest that the transition state (TS) for transfer to the pump-site should be positively charged, while the one for transfer to the binuclear center should be charge-neutral. The character of the former TS will guarantee that the protons will be pumped to the outside and not return to the inside, while the neutral character of the latter one will allow transfer with a sufficiently low barrier. In the simple electrostatic analysis, leading to this qualitative picture of the pumping process, the results from the kinetic experiments are strictly followed, but it is at least as important to follow the fundamental requirements for pumping. In this perspective, the uncertainties in the quantitative analysis should be rather unimportant for the emerging qualitative picture of the pumping mechanism. The second problem addressed concerns the purpose of the K-channel. It is argued that the reason for the presence of the K-channel could be that protons cannot pass through the binuclear center at some stage of pumping. Barriers and water binding energies were computed using hybrid density functional theory (DFT) to investigate this question.