  We consider for the first time the leading large top mass corrections,
arising at higher order in electroweak interactions, to the rare decays
$K\to\pi\nu\bar\nu$ and the related modes $B\to X_s\nu\bar\nu$ and $B\to
l^+l^-$. Higher order effects of similar type have previously been calculated
in the large-$m_t$ limit for key observables of precision electroweak physics
at Z-factories. Here we obtain the corresponding corrections of order ${\cal
O}(G^2_F m^4_t)$ at the amplitude level for short-distance dominated rare meson
decays. This allows us to quantify the importance of higher order electroweak
effects for these processes, which can be reliably computed and have very small
uncertainties from strong interactions. Simultaneously it becomes possible to
remove, to some extent, ambiguities in the definition of electroweak parameters
describing the strength of FCNC interactions. The corrections we discuss are at
the level of a few percent.
