The total cross section for electron-positron annihilation into hadrons
is calculated in the region just below the B meson threshold. QCD
corrections up to third order, quark mass effects, initial state
radiation, the running of alpha_QED and the tails of the Upsilon resonances are
included in the prediction. For given alpha_s the prediction is accurate
to 0.5 percent. An experimental measurement with the corresponding
precision would allow to determine alpha_s with high accuracy at
intermediate energies.