Modern switched adaptive predictors such as Gradient Adjusted Predictor (GAP) estimates the slope of pixels from the prediction context of a unknown pixel. Based on this slope, the unknown pixels is predicted. But slope alone can not characterize some of the more complex relationship between the predicted pixel and its prediction context. In this work, this complex relationship is found in terms of a statistically valid sixth order predictor, which is used for predicting pixels under various slope conditions in the GAP frame work. It is seen through simulations, that the average entropy of the residual images is reduced significantly, when applied on high resolution images. The computational cost of the proposed method is almost of the same order as that of the GAP and requires the same previous two line buffering while coding. © 2005 IEEE.