This paper proposes a transform-based compression algorithm for waveforms associated with power quality and transient phenomena in power systems. This method uses the wavelet transform, a dynamic bit allocation in the transform domain through estimation of the spectral shape, as well as entropy coding in order to minimize residual redundancy. Five distinct approaches for estimating the spectral shape are proposed. Four of them are based on analytical models that seek to describe the decreasing behavior of the transformed coefficients: (1) decreasing linear bit allocation shape; (2) decreasing quadratic bit allocation shape; (3) decreasing exponential bit allocation shape; (4) rotated sigmoid bit allocation shape; and (5) the fifth approach-the neural shape estimator (NSE)-is an adaptive model that uses an artificial neural network to map the changes in the spectrum shape. Results with databases of real signals and a performance evaluation using objective measures are reported. The results indicate that the NSE approach outperforms the other proposed solutions that use spectral shape estimation for coding, as well as other compression contributions reported in the literature.