We search for standard model single-top-quark production in the W-gluon fusion and W⋆ channels using 106pb-1 of data from pp¯ collisions at s√=1.8 TeV collected with the Collider Detector at Fermilab. We set an upper limit at 95% confidence level (C.L.) on the combined W-gluon fusion and W⋆ single-top cross section of 14 pb, roughly six times larger than the standard model prediction. Separate 95% C.L. upper limits in the W-gluon fusion and W⋆ channels are also determined and are found to be 13 and 18 pb, respectively.