In this paper, we study a suitable experimental design of electrochemical impedance spectroscopy (EIS) to reduce the number of frequency points while not significantly affecting the uncertainties of the estimated cell's equivalent circuit model (ECM) parameters. It is based on an E-optimal experimental design that aims to maximize the information about the ECM parameters collected by EIS measurements and, at the same time, minimize the overall uncertainty. In a numerical experiment, we first analyze to which extent reducing the number of measurement points at low frequencies affects the uncertainty of the estimated parameters. Secondly, we show that applying the frequency adjustments can lead to the same or even improved global uncertainty of ECM parameter estimates as with a higher number of measurements. This is numerically verified through a case study using the ECM parameters of a commercial battery cell.