  We investigate minimal-perimeter configurations of two finite sets of points
on the square lattice. This corresponds to a lattice version of the classical
double-bubble problem. We give a detailed description of the fine geometry of
minimisers and, in some parameter regime, we compute the optimal perimeter as a
function of the size of the point sets. Moreover, we provide a sharp bound on
the difference between two minimisers, which are generally not unique, and use
it to rigorously identify their Wulff shape, as the size of the point sets
scales up.
