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 gq-->tb[over ]q;{'}, keeping the b-quark mass nonzero. 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(Q2/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.