  We study the energy spectrum of bottomonium in perturbative QCD, taking
alpha_s(Mz)=0.1181 +/- 0.0020 as input and fixing m_b^{MSbar}(m_b^{MSbar}) on
the Upsilon(1S) mass. Contrary to wide beliefs, perturbative QCD reproduces
reasonably well the gross structure of the spectrum as long as the coupling
constant remains smaller than one. We perform a detailed analysis and discuss
the size of non-perturbative effects. A new qualitative picture on the
structure of the bottomonium spectrum is provided. The lowest-lying (c,cbar)
and (b,cbar) states are also examined.
