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For secure communications over wireless fading channels, the secrecy outage probability is widely used as the performance measure. However, the current secrecy outage formulation has two major limitations in evaluating the secrecy performance: a) the amount of information leakage to the eavesdropper cannot be characterized when an outage occurs, b) the current formulation does not give insights into the eavesdropper's decodability of confidential messages. To overcome such limitations and obtain in-depth understanding of secrecy performance over wireless fading channels, this paper proposes three new secrecy measures for different practical aims, namely, 1) generalized secrecy outage probability, 2) asymptotic lower bound on eavesdropper's decoding error probability, and 3) average information leakage rate. A specific example of wireless transmissions with a fixed-rate wiretap code is given to …