Sinusoidal modeling is traditionally one of the most popular techniques for low bitrate audio coding. Usually, the sinusoidal parameters are kept constant within a time segment but the exponentially damped sinusoidal (EDS) model is also an efficient alternative. However, the inclusion of an additional damping parameter calls for a specific quantization scheme. In this paper, we propose an asymptotically optimal entropyconstrained quantization method for amplitude, phase and damping parameters. We show that this scheme is nearly optimal in terms of rate-distortion trade-off. We also show that damping consumes the smallest part of the total entropy of quantization indexes, which suggests that the EDS model is truly efficient for audio coding.