Generalized Pareto distributions (GPD) are frequently applied for the statistical analysis of extreme wind speeds. A central topic in extreme-value theory is the adaptive estimation of the extreme-value index γ. Several authors have demonstrated a high sensitivity of γ against the threshold when analyzing extreme wind speeds. This undesirable effect introduces the difficulty to provide reliable quantile estimates. This paper aims to bring this problem to meteorologists and proposes a stable estimator (the Zipf estimator) for γ. This could allow a more objective prior identification of the sign and range of γ. The method is based on regression in the so-called generalized quantile plots. A comparative study with a classical estimator (the probability-weightedmethod) is made and it is shown that the Zipf estimator significantly decreases the variance in the calibration of the GPD to extreme wind gusts. Finally, the new methodology is applied to get improved prediction of extreme wind gusts in Belgium.