A 1-bit adaptive decision-feedback predictive coding (ADFPC) system is derived on the assumption of ‘good’ decisions. The predictor in the ADFPC is made adaptive by projecting the gradient, at each iteration, along the co-ordinate which exhibits the maximum absolute gradient. This gradient-seeking method requires that the stepsize only needs to be optimum with respect to a single coefficient (co-ordinate) during each iteration. A formula for calculating the stepsize at each iteration is obtained via a minimisation of the squared prediction error. Simulation results obtained in the encoding of a 1st-order autoregressive source and a monochrome image (with the analogue sources digitised by a 6-bit quantiser prior to encoding) reveal that the ADFPC is robust and exhibits good performance.