  We consider sets in $\mathbb R^N$ which minimise, for fixed volume, the sum
of the perimeter and a non-local term given by the double integral of a kernel
$g:\mathbb R^N\setminus\{0\}\to \mathbb R^+$. We establish some general
existence and regularity results for minimisers. In the two-dimensional case we
show that balls are the unique minimisers if the perimeter-dominated regime,
for a wide class of functions $g$.
