  We show that a lower bound for covariance of $\min(X_1,X_2)$ and
$\max(X_1,X_2)$ is $\cov{X_1}{X_2}$ and an upper bound for variance of \\
$\min(X_2,\max(X,X_1))$ is $\var{X} + \var{X_1} +\var{X_2}$ generalizing
previous results. We also characterize the cases where these bounds are sharp.
