It is shown that the potential for lepton-antilepton bound
states (leptonium) is the Fourier transform of the first Born
approximation to the QED scattering amplitude in an 8-component
equation, while 16-component equations are excluded.
The Fourier transform is exact at all {\sl cms} energies
$ - \infty < E < \infty$; the resulting atomic spectrum is
explicitly CPT-invariant.
