  We call a family of sets intersecting, if any two sets in the family
intersect. In this paper we investigate intersecting families $\mathcal{F}$ of
$k$-element subsets of $[n]:=\{1,\ldots, n\},$ such that every element of $[n]$
lies in the same (or approximately the same) number of members of
$\mathcal{F}$. In particular, we show that we can guarantee $|\mathcal{F}| =
o({n-1\choose k-1})$ if and only if $k=o(n)$.
