To reduce the computational requirement which two-dimensional transform coding imposes it is common to combine the one-dimensional form of the process with simple previous-element predictive coding with an assumed fixed value of predictor coefficient for all coefficients. The underlying assumptions of this approach are here examined both theoretically and with reference to experimental data obtained from two widely different real images, and it is shown that it is highly inefficient to apply the prediction process to all of the transform coefficients, because not only is the error sequence variance frequently greater than that of the original coefficient sequence, but also considerable residual correlation exists in the signal to be quantised and coded, thus undermining the basis upon which such a data-compression technique rests.