We use a neural-network technique to search for standard model single-top-quark production in the 106pb-1 dataset accumulated by the Collider Detector at Fermilab detector during the 1992–1995 collider run (“run I”). Using a sample of 64 W+1, 2, 3 jets events, we set a 95% confidence level upper limit of 24 pb on the W-gluon and W∗ combined single-top cross section.