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Secrecy on the physical layer is a promising technique to simplify the overall cross-layer secrecy concept. In many recent works on the multiple antenna wiretap channel, perfect channel state information to the intended receiver as well as the passive eavesdropper are assumed. In this paper, the transmitter has only partial information about the channel to the eavesdropper, but full information on the main channel to the intended receiver. The applied channel model is the flat-fading multiple-input single-output wiretap channel. We minimize the outage probability of secure transmission under single-stream beamforming and the use of artificial noise in the null space of the main channel. Furthermore, we derive a suboptimal beamforming scheme based on a Markov bound, which performs reasonably well. The results generalize the cases with perfect as well as without channel state information of the eavesdropper channel. Numerical simulations illustrate the secrecy outage probability over the degree of channel knowledge and confirm the theoretical results.