  We introduce and explore a natural rank for totally disconnected locally
compact groups called the bounded conjugacy rank. This rank is shown to be a
lattice invariant for lattices in sigma compact totally disconnected locally
compact groups; that is to say, for a given sigma compact totally disconnected
locally compact group, some lattice has bounded conjugacy rank n if and only if
every lattice has bounded conjugacy rank n. Several examples are then
presented.
