  The paper concerns the tree invariants of string links, introduced by
Kravchenko and Polyak and closely related to the classical Milnor linking
numbers also known as $\bar{\mu}$--invariants. We prove that, analogously as
for $\bar{\mu}$--invariants, certain residue classes of tree invariants yield
link homotopy invariants of closed links. The proof is arrow diagramatic and
provides a more geometric insight into the indeterminacy through certain tree
stacking operations. Further, we show that the indeterminacy of tree invariants
is consistent with the original Milnor's indeterminacy. For practical purposes,
we also provide a recursive procedure for computing arrow polynomials of tree
invariants.
