Additive Increase Multiplicative Decrease (AIMD) is a widely used congestion control algorithm that is known to be fair and efficient in utilizing the network resources. In this paper, we revisit the performance of the AIMD algorithm under realistic conditions by extending the seminal model of Chui~\etal. We show that under realistic conditions the fairness and efficiency of AIMD is sensitive to changes in network conditions. Surprisingly, the root cause of this sensitivity comes from the way the congestion window is rounded during a multiplicative decrease phase. For instance, the floor function is often used to round the congestion window value because either kernel implementations or protocol restrictions mandate to use integers to maintain system variables. To solve the sensitivity issue, we provide a simple solution that is to alternatively use the floor and ceiling functions in the computation of the congestion window during a multiplicative decrease phase, when the congestion window size is an odd number. We observe that with our solution the efficiency improves and the fairness becomes one order of magnitude less sensitive to changes in network conditions.