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Sinusoidal modeling is one of the most popular techniques for low bitrate audio coding. Usually, the sinusoidal parameters (amplitude, pulsation and phase of each sinusoidal component) are kept constant within a time segment. An alternative model, the so-called Exponentially-Damped Sinusoidal (EDS) model, includes an additional damping parameter for each sinusoidal component to better represent the signal characteristics. It was however never shown that the EDS model could be efficient for perceptual audio coding. To that aim, we propose in this paper an efficient analysis/synthesis framework with dynamic time-segmentation on transients and psychoacoustic modeling, and an asymptotically optimal entropy-constrained quantization method for the four sinusoid parameters (e.g., including damping). We then apply this coding technique to real audio excerpts for a given entropy target corresponding to a low bitrate (20 kbits/s), and compare this method with a classical sinusoidal coding scheme using a constant-amplitude sinusoidal model and the perceptually weighted Matching Pursuit algorithm. Subjective listening tests show that the EDS model is more efficient on audio samples with fast transient content, and similar to the classical model for more stationary audio samples.