In the presence of plant-model mismatch, the estimation of plant gradients is key to the performance of measurement-based iterative optimization schemes. However, gradient estimation requires time-consuming experiments, wherein the plant is sequentially perturbed in all input directions. To ease this gradient estimation task, it has been proposed to exploit the sensitivity of the model gradient with respect to the model parameters to find a reduced input subspace that is spanned by a few privileged directions for gradient estimation. The computation of gradient sensitivities to parametric variations requires the evaluation of double derivatives with respect to both the inputs and the parameters. In this short note, we propose an approach for computing the privileged directions using only single derivatives with respect to the inputs. We show that this approach results in significant reduction in computational costs without compromising the quality of the privileged directions. (C) 2019 Elsevier Ltd. All rights reserved.