  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^-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^+1.5_-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^2
in case the mass of the right-handed neutrino is smaller than the mass of the
right-handed W^\prime or 790 GeV/c^2 in the opposite case.
