  We describe the ordering of a class of clones by minion homomorphisms, also
known as minor preserving maps or height 1 clone homomorphisms. The class
consists of all clones on finite sets determined by binary relations whose
projections to both coordinates have at most two elements. This class can be
alternatively described up to minion homomorphisms as the class of multisorted
Boolean clones determined by binary relations. We also introduce and apply the
concept of a minion core which provides canonical representatives for
equivalence classes of clones, more generally minions, on finite sets.
