  Using the Laplace sum rule (LSR) approach, which is less affected by the
contribution of the higher mass hadronic states than the Finite Energy Sum Rule
(FESR), we test the reliability of the existing estimate of the
$K^0$-$\overline {K}^0$ mixing parameter from the four-quark two-point
correlator. We obtain, for the renormalization group invariant $B$-parameter
$\Big[ f_K/(1.2f_\pi)\Big]^2 \hat {B}_K$, the upper bound: 0.83 and the $best$
estimate: $0.55 \pm 0.09$. Combining the previous estimate with the updated
value of $f_B\sqrt{B_B}=(1.49\pm 0.14)f_\pi$ obtained from the same LSR method,
one can deduce the $best$ fitted values $(\rho,\eta)\approx (0.41,0.09)$ of the
CKM parameters.
