Heavy-tailed distributions are used in various areas of statistical applications. An important parameter for such distributions is the tail coefficient. Many estimators have been developed for that coefficient, with the Hill estimator perhaps the most well-known one. However, the Hill estimator as well as improved versions that are based on it, all rely on asymptotic expansions that are unlikely to hold for small samples. In this paper we introduce a new approach to the tail coefficient estimation in the case of Weibull-type distributions in order to address the small sample issues. A simulation is carried out to study the properties of the new estimator, namely its bias and the mean squared error, and to compare them to those of some existing estimators.