In this paper we present new results from single-top-quark searches with the CDF II detector at the Fermilab Tevatron. In a data sample of 162 pb-1 of proton-antiproton collisions accumulated at CDF, we find no significant evidence for signal and set an upper limit of 17.8 pb on the total single-top production rate, at 95% confidence level. Individual upper limits of 10.1 pb and 13.6 pb are set on the the individual rates of t–channel, and s–channel single-top, respectively.