In this paper, we present a decomposition for sinusoidal coding of audio, based on an amplitude modulation of sinusoids via a linear combination of arbitrary basis vectors. The proposed method, which incorporates a perceptual distortion measure, is based on a relaxation of a nonlinear least-squares minimization. Rate-distortion curves and listening tests show that, compared to a constant-amplitude sinusoidal coder, the proposed decomposition offers perceptually significant improvements in critical transient signals.