Data from e+e- annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 and 44 GeV were used to study the 4-jet rate using the Durham algorithm as well as the first five moments of event shape observables. The data were compared with NLO QCD predictions, augmented by resummed NLLA calculations for the 4-jet rate, in order to extract values of the strong coupling constant alpha_S. The preliminary results are alpha_S(MZ) = 0.1169 +/- 0.0026 (4-jet rate) and alpha_S(MZ) = 0.1286 +/- 0.0072 (moments) consistent with the world average value. For some of the higher moments systematic deficiencies of the QCD predictions are observed.
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