B\'ar\'any showed that there is a constant $c_d>0$
such that if $S$ is any $n$-point set in $R^d$, then there exists
a point in $c_d$ fraction of simplices spanned by $S$.
We present a simple construction of a point set for which there is
no point contained in many simplices. The construction is optimal
for $d=2$ and gives the first non-trivial upper bounds on $c_d$ for
$d\geq 3$. We will also discuss generalizations to stabbing simplices
by affine spaces. Joint work with Ji\v{r}\'\i{} Matou\v{s}ek
and Gabriel Nivasch.