Secrecy on the physical layer receives increased research interest. Especially in the wireless communication scenarios, the interest in confidentiality of messages increases. In this paper, we discuss the effectiveness of the beamforming strategies maximum ratio transmission (MRT), zero forcing (ZF), and an optimized beamforming (BF) strategy for the transmission under secrecy constraints. The applied channel model is the flat-fading MISO (multiple-input single-output) wiretap channel, where the channel to the eavesdropper is only partly known at the transmitter. The scenario with perfect and no channel information to the eavesdropper are included as special cases. We show that under certain conditions the achievable secrecy rates for the transmission with optimized beam-forming can be increased by transmitting artificial noise (AN) in the null space of the channel to the intended receiver, which produces additional interference only at the eavesdropper. We provide a characterization of the optimal beamforming and artificial noise beamforming and analyze the optimal power allocation for asymptotic cases (low and high SNR as well as no and perfect channel information). Numerical simulations illustrate the results.