In this paper, secure transmission of information over an ergodic fading channel is studied in the presence of statistical quality of service (QoS) constraints. We employ effective capacity to measure the secure throughput of the system, i.e., effective secure throughput. We assume that the channel side information (CSI) of the main and the eavesdropper channels is available at the transmitter side. Under this assumption, we investigate the optimal power control policies that maximize the effective secure throughput. In particular, it is noted that opportunistic transmission is no longer optimal and the transmitter should not wait to send the data at a high rate until the main channel is much better than the eavesdropper channel. Moreover, it is shown that the benefits of adapting the power with respect to the CSI of both the eavesdropper and main channels rather than the CSI of only the main channel diminish as QoS constraints become more stringent.