The authors have performed a fully differential calculation of QCD corrections to electroweak production of single top quarks. The method used allows for jet definitions and experimental cuts. The corresponding computer code passes the necessary check of reproducing the previously known total rate. First examination of the rapidity and transverse momentum of the top quark shows the corrections to be flat relative to leading order. Additional phenomenological studies are in order. Further work is in progress on the corrections to t-b-jet final states which will give a comprehensive set of tools for studying single-top-quark production at future hadron-hadron colliders.