An enhanced deterministic model along with a stochastic model for describing clock noise is used to compute predictions of the time-offset of individual GPS satellites from the IGS rapid timescale. These are determined with significantly lower prediction uncertainties than may currently be obtained using the IGS ultra-rapid predictions. At prediction length of one day IGS prediction errors are commonly of the order of several ns for all GPS satellite clocks. In comparison the new techniques offer to limit prediction errors at the order of 1 ns for prediction lengths of one day in the newer generation Block IIR and IIF satellites. The factors contributing to the uncertainties in the IGS predictions are discussed. The application of a Kalman filter based prediction algorithm is shown to produce close to optimal predictions.