  We directly fit the QCD dimensional transmutation parameter, Lambda MS-bar,
to experimental data on e+e- jet observables, making use of next-to-leading
order (NLO) perturbative calculations. In this procedure there is no need to
mention, let alone to arbitrarily vary, the unphysical renormalisation scale
mu, and one avoids the spurious and meaningless ``theoretical error''
associated with standard alpha_s determinations. PETRA, SLD, and LEP data are
considered in the analysis. An attempt is made to estimate the importance of
uncalculated next-NLO and higher order perturbative corrections, and power
corrections, by studying the scatter in the values of Lambda MS-bar obtained
for different observables.
