  The rare K -> pi nu anti-nu decays play a central role in testing the
Standard Model and its extensions. Upcoming experiments plan to measure the
decay rates with high accuracy. Yet, unknown higher-order electroweak
corrections result in a sizeable theory error. We remove this uncertainty by
computing the full two-loop electroweak corrections to the top-quark
contribution X_t to the rare decays K_L -> pi0 nu anti-nu, K+ -> pi+ nu
anti-nu, and B -> X_{d,s} nu anti-nu in the Standard Model. The remaining
theoretical uncertainty related to electroweak effects is now far below 1%.
Finally we update the branching ratios to find Br(K_L -> pi0 nu anti-nu) =
2.43(39)(6) * 10^-11 and Br(K+ -> pi+ nu anti-nu) = 7.81(75)(29) * 10^-11. The
first error summarises the parametric, the second the remaining theoretical
uncertainties.
