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The parameter epsilon_K, that quantifies CP violation in kaon mixing, is theobservable setting the strongest constraints on new physics with a genericflavour and CP structure. While its experimental uncertainty is at the halfpercent level, the theoretical one is at the level of 15%. One of the largestsources of the latter uncertainty is the poor perturbative behaviour of theshort-distance contribution of the box diagram with two charm quarks. In thisproceeding, based on arXiv:1602.08494, I summarise how that contribution can beremoved, from the imaginary part of the mixing amplitude, by a rephasing of thekaon fields. A first outcome is a mild reduction of the total theoreticaluncertainty of epsilon_K: while this might look counterintuitive at firstsight, if different "pieces" (i.e. short- and long-distance) of an observableare computed with different techniques, then it is possible to choose a phaseconvention where the total uncertainty of that observable is optimised.Moreover, it is worthy to discuss if and how this freedom of rephasing, whichhas been somehow overlooked in the past, can help in making progress in latticeQCD computations of immediate relevance for epsilon_K.

Epsilon_K in the Standard Model and the kaon phase conventions