  We analyse the subleading non-resonant contributions to the e+ e- -> W+ W- b
bbar cross section at energies near the top-antitop threshold. These correspond
to next-to-next-to-leading-order (NNLO) corrections with respect to the
leading-order resonant result. We show that these corrections produce 1/epsilon
endpoint singularities which precisely cancel the finite-width divergences
arising in the resonant production of the W+ W- b bbar final state from
on-shell decays of the top and antitop quarks at the same order. We also
provide analytic results for the (m_t/Lambda)^2, (m_t/Lambda) and
(m_t/Lambda)^0 log(Lambda) terms that dominate the expansion in powers of
(Lambda/m_t) of the complete set of NNLO non-resonant corrections, where Lambda
is a cut imposed on the invariant masses of the b W pairs that is neither too
tight nor too loose (m_t Gamma_t << Lambda^2 << m_t^2).
