In this paper, methods for improved parametric coding of transients are presented. We propose a signal model for coding of transients consisting of a sum of sinusoids each being amplitude-modulated by a different gamma envelope. These envelopes are characterized by an onset time, an attack and a decay parameter. An efficient method for estimating these parameters is presented. Further, methods are proposed that combine this transient model with a constant-amplitude sinusoidal model in order to achieve efficient coding of both stationary and transient signal parts. By rate-distortion optimization using a perceptual distortion measure we combine variable rate bit allocation and segmentation in an optimal way. Formal as well as informal listening tests show that significant improvements can be achieved with the proposed model as compared to a state-of-the-art sinusoidal coder by the combination of optimal segmentation and amplitude modulated sinusoidal audio coding.