We search for Standard Model single-top-quark production in the
W-gluon fusion and W* channels using 106 pb-1 of data from p anti-p
collisions at s**(1/2) = 1.8 TeV collected with the Collider Detector at
Fermilab. We set an upper limit at 95% C.L. on the combined Wg + W*
single-top cross section of 13.5 pb, roughly five-and-a-half times larger
than the standard model prediction. Separate 95% C.L. upper limits in the
Wg-fusion and W* channels are also determined and are found to be 13.5 and
12.9 pb respectively.