We present a novel dual-mode MPC scheme that significantly reduces the computational effort of robust MPC (RMPC). Specifically, we propose a method for the computation of a large set C on which no optimal control problem (OCP) needs to be solved online. The method is motivated by the trivial observation that, for classical MPC, no optimization is required for the states in the terminal set T, because the unconstrained linear-quadratic regulator is optimal there. While this observation cannot be directly transferred to RMPC, we show that suitable sets C exist in the neighborhood of T and state an algorithm for their computation. We stress that the resulting sets C are significantly larger than robust positively invariant sets that are typically exploited in RMPC and on which it is well-known that no OCP needs to be solved online. The approach is illustrated with three examples for which we observe a reduction of the numerical effort between 22.36% and 95.60%. (C) 2018 Elsevier Ltd. All rights reserved.