Local electrochemical impedance spectroscopy (LEIS) is a promising technique for the characterization of heterogeneous surface reactivity. Significant development of LEIS relies on the improvement of the spatial resolution for reaching the micrometer scale. This work presents the influence of the probe size, especially in the high frequency domain where an inductive-like response ascribed to the stray dielectric capacitance between the two electrodes of the probe used for performing the local current measurement can be observed. A detailed analysis of the whole set-up (electrode geometry and measuring device) allows an analytical expression of the impedance for the whole system to be obtained. Based on the analysis of this expression and on experimental results, two different strategies have been proposed to cancel the HF time constant: a post treatment of the results via a preliminary electrical characterization of the local probe or the minimization of the electrolyte resistance by measuring the local potential in the close vicinity of the substrate. Both approaches were shown to be efficient. (C) 2017 Elsevier Ltd. All rights reserved.