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.