In Gardes et al. (2011), a new family of distributions is introduced, depending on two parameters tau and theta which encompasses Pareto-type distributions as well as Weibull tail-distributions. Estimators for theta and extreme quantiles are also proposed, but they both depend on the unknown parameter tau, making them useless in practical situations. In this paper, we propose an estimator of tau which is independent of theta. Plugging our estimator of tau in the two previous ones allows us to estimate extreme quantiles from Pareto-type and Weibull tail-distributions in an unifi ed way. The asymptotic distributions of our three new estimators are established and their efficiency is illustrated on a small simulation study and on a real data set.