  The preceding experimental and theoretical results on the rare decay $\pi^0
\to e^+e^-$ are briefly summarized. Already computed two-loop QED corrections
are reviewed and the bremsstrahlung contribution beyond the soft-photon
approximation is analytically calculated. The possible further contribution of
QCD loop corrections is estimated using the leading logarithm approximation.
The complete result can be used to fit the value of the contact interaction
coupling $\chi^r$ to the recent KTeV experiment with the result $\chi^r(M_\rho)
= 4.5 \pm 1.0$.
