This paper proposes efficient step response model implementation strategies that lead to accurate control and high computational performance in an embedded Model Predictive Control (MPC) scheme. Different implementations of the step response prediction model are examined, and inherent properties that directly affect control performance in the presence of disturbances are discussed. Model errors that are inconsistent with bias updates (i.e. the model of unknown disturbances commonly used in step response MPC) are identified, and it is shown that the bias updates may worsen the effect of the errors in some cases. Particular attention is paid to the robustness of the prediction models to small truncation errors and errors in the input or measured disturbance history. Several implementation aspects that are crucial for embedded targets with limited resources are discussed. The findings are illustrated by simple simulation examples and an industrial case-study involving hardware-in-the-loop simulation of a subsea compact separation process. (C) 2016 Elsevier Ltd. All rights reserved.