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The latest H.264/AVC video coding standard achieves high compression rates in exchange for high computational complexity. Nowadays, however, many application scenarios require the encoder to meet some complexity constraints. This paper proposes a novel complexity control method that relies on a hypothesis testing that can handle time-variant content and target complexities. Specifically, it is based on a binary hypothesis testing that decides, on a macroblock basis, whether to use a low- or a high-complexity coding model. Gaussian statistics are assumed so that the probability density functions involved in the hypothesis testing can be easily adapted. The decision threshold is also adapted according to the deviation between the actual and the target complexities. The proposed method is implemented on the H.264/AVC reference software JM10.2 and compared with a state-of-the-art method. Our experimental results prove that the proposed method achieves a better trade-off between complexity control and coding efficiency. Furthermore, it leads to a lower deviation from the target complexity.