  We present the predictions at next-to-leading order (NLO) in the strong
coupling for the single-top cross section in the t channel at the Tevatron and
the LHC. Our calculation starts from the 2 -> 3 Born amplitude g q -> t bbar
q', keeping the b-quark mass non-zero. A comparison is performed with a
traditional NLO calculation of this channel based on the 2 -> 2 Born process
with a bottom quark in the initial state. In particular, the effect of using
kinematic approximations and resumming logarithms of the form log(Q^2/m_b^2) in
the 2 -> 2 process is assessed. Our results show that the 2 -> 3 calculation is
very well behaved and in substantial agreement with the predictions based on
the 2 -> 2 process.
