Soft and collinear gluon radiation is important for many applications in QCD. Classical examples are the two-jet region in e+e- and the large-x limit in deep-inelastic scattering. In such cases, the perturbative expansion breaks down due to large Sudakov logs, which must be resummed. The standard power-correction expansion breaks down as well. We suggest a new method which copes with both the perturbative and the non-perturbative aspects. Dressed Gluon Exponentiation (DGE) combines renormalon resummation with the exponentiation property in the Sudakov region. As opposed to the standard fixed logarithmic accuracy resummation, the DGE exponent is renormalization scale invariant. It is shown that sub-leading logs, which are usually neglected, are factorially enhanced and must be resummed prior to any non-perturbative correction. We use the thrust distribution is e+e- annihilation as an example, showing that comparison with experimental data can be achieved without any hadronization model well inside the two-jet region.