  Rare flavour-changing neutral-current transitions of the type $s \to d
\ell^+\ell^-(\nu\bar\nu)$ and $b \to s \ell^+\ell^-(\nu\bar\nu)$ are analysed
in supersymmetric extensions of the Standard Model with generic flavour
couplings. It is shown that these processes are particularly sensitive to the
left--right mixing of the squarks and that, in the presence of non-universal
$A$ terms, they could lead to unambiguous signatures of new physics in
exclusive $K$ and $B$ meson decays.
