Image and audio data are examples of domains in which DPCM (Differential Pulse Coded Modulation) is an effective method for removing much of the linear correlation between data samples. However, most simple DPCM schemes cannot simultaneously cater for smooth signals, noisy signals, and discontinuities such as edges in images. To overcome this, many adaptive DPCM schemes have been proposed, including median predictors, gradient-based switching predictors and gradient-based blending predictors. In this paper we generalize the idea of blending predictors, and describe a powerful technique for creating locally adaptive compound predictors. The result is a prediction scheme which works well over a range of data types froms smooth to noisy, and requires very few tunable parameters. We apply this scheme to greyscale image data, colour image data, and audio data, and compare results with some of the current best adaptive DPCM predictors.