A recent analysis by the DELPHI collaboration showed that if one uses an "optimised" choice of renormalization scale, some e+e(^-) event shape means can be described without significant power corrections. Motivated by this, in this thesis optimised scales (and schemes) are applied to similar observables. First, abrief review of QCD and scale/scheme optimisation is given. Then, the distributions of the e+e(^-) event shapes l-thrust and heavy-jet mass are studied within the Method of Effective Charges, including performing a next-to-leading log resummation of the effective charge beta function. There is some reduction in the apparent size of power corrections, but the resummed results behave pathologically in the 2-jet limit. Next, the Principle of Minimal Sensitivity is applied to the choice of renormalization and factorization scales for event shape means defined in the Breit frame of ep BIS. This has little effect on the perturbative predictions and large power corrections are still required. However, if one introduces separate renormalization scales for the qγ* and gγ* sub-processes, a substantial reduction in the size of the power corrections is seen for most observables.