This work examines the advantages of having only channel state information at the transmitter (CSIT), and not at the receiver and the eavesdropper, when achieving secrecy in fading wiretap channels. The key idea is that, with only CSIT, the transmitter can pre-compensate for the amplitude and phase distortions on the main channel. This allows the receiver to decode coherently even without knowledge of the CSI, while leaving the eavesdropper confused by the unknown variations of its own channel. When the channel is reciprocal, this CSI assumption can be achieved in practice through reverse training, i.e., by having the receiver emit the training signal so that the transmitter can estimate the channel by itself. Two secrecy-enhancing transmission schemes are proposed to exploit the CSIT. The truncated channel inversion scheme is used when the receiver and the eavesdropper have no CSI available, and the truncated phase compensation scheme is adopted when they can practically measure the SNR. The achievable secrecy rates of these schemes are derived for both single-antenna and multi-antenna wireless fading scenarios. Numerical results show significant improvements in secrecy rate compared to the case with full CSI at all terminals.