  We consider the "homotopy coniveau tower" for an arbitrary cohomology theory
on smooth varieties over a field or a Dedekind domain. This tower is a
generalization of the construction used by Bloch-Lichtenbaum and
Friedlander-Suslin in their studies of the spectral sequence from motivic
cohomology to K-theory. Our main result is that an application of the classical
Chow's moving lemma and some categorical constructions make the homotopy
coniveau tower strictly functorial when the base is a field, and functorial in
the homotopy category when the base is a Dedekind domain.
