  We study cocompact lattices with dense projections in a product $G_1 \times
G_2$ of locally compact groups and show, under the assumption that each $G_i$
is a closed subgroup of the automorphism group $Aut(T_i)$ of a regular tree
satisfying certain local transitivity conditions, that such a lattice is
contained in only finitely many discrete subgroups of $G_1 \times G_2$.
