In this paper, a new predictor-based control strategy for LTI systems with input delay and unknown disturbances is proposed. The disturbing signal and its derivatives up to the r-th order are estimated by means of an observer, and then used to construct a prediction of the disturbance. Such prediction allows defining a new predictive scheme that takes into account its effect. Also, a suitable transformation of the control input is presented and a performance analysis is carried out to show that, for a given controller, the proposed solution leads to better disturbance attenuation than previous approaches in the literature for smooth enough perturbations. (C) 2016 Elsevier Ltd. All rights reserved.