A low entropy pyramidal image data structure suited for lossless coding and progressive transmission is proposed in this work. The new coder, called the progressively predictive pyramid (PPP) is based on the well-known Laplacian pyramid. By introducing inter-resolution predictors into the original Laplacian pyramid, we show that the entropy level in the original pyramid can be reduced significantly. To take full advantage of progressive transmission, a scheme is introduced to create the predictor adaptively, thus eliminating the need to transmit the predictor and reducing the coding overheads. A method for designing the predictor is presented. Numerical results show that PPP is superior to traditional approaches to pyramid generation in the sense that the pyramids generated by PPP always have significantly lower entropy values.