  We consider weights $w$ and their cut-offs: $w_a(t)=w(t)$ if $w(t)\le a$ and
$w_a(t)=a$ if $w(t)> a$. We consider a generalized $A_p$-``norm'' and prove
that the ``norm'' of $w_a$ is not greater then the ``norm'' of $w$. Our proof
in the case $w\in A_2$ is especially simple.
