  Static black holes of dilaton-axion gravity become singular in the extreme
limit, which prevents a direct determination of their near-horizon geometry.
This is addressed by first taking the near-horizon limit of extreme rotating
NUT-less black holes, and then going to the static limit. The resulting
four-dimensional geometry may be lifted to a Bertotti-Robinson-like solution of
six-dimensional vacuum gravity, which also gives the near-horizon geometry of
extreme Kaluza-Klein black holes in five dimensions.
