This article reports on recent searches for single-top-quark production by the CDF collaboration at the Tevatron using a data set that corresponds to an integrated luminosity of 955 pb(sup -1). Three different analyses techniques are employed, one using likelihood discriminants, one neural networks and one matrix elements. The sensitivity to single-top production at the rate predicted by the standard model ranges from 2.1 to 2.6 (sigma). While the first two analyses observe a deficit of single-top like events compared to the expectation, the matrix element method observes an excess corresponding to a background fluctuation of 2.3 (sigma). The null results of the likelihood and neural network analyses translate in upper limits on the cross section of 2.6 pb for the t-channel production mode and 3.7 pb for the s-channel mode at the 95% C.L. The matrix element result corresponds to a measurement of 2.7(sup +1.5)(sub -1.3) pb for the combined t- and s-channel single-top cross section. In addition, CDF has searched for non-standard model production of single-top-quarks via the s-channel exchange of a heavy W(prime) boson. No signal of this process is found resulting in lower mass limits of 760 GeV/c(sup 2) in case the mass of the right-handed neutrino is smaller than the mass of the right-handed W(prime) or 790GeV/c(sup 2) in the opposite case.