A modification of the Parameterized Tube Model Predictive Control (PTMPC) strategy for linear systems with additive disturbances is proposed, which reduces the dependence of the number of optimization variables on horizon length from quadratic to linear by using a triangular striped prediction structure. Unlike PTMPC, which assumes a fixed linear terminal feedback law for predictions, the proposed prediction scheme allows disturbance compensation to extend beyond the initial N-step prediction horizon. The resulting scheme can potentially outperform PTMPC in terms of the size of the domain of attraction and allows for a longer horizon N for the same computational demand. (C) 2016 Elsevier Ltd. All rights reserved.