Let k be a perfect field and M a strictly homotopy invariant sheaf of abelian groups on Sm_k. The cousin complex can be used to compute the cohomology of a smooth variety X over k with coefficients in M. However, if X --> Y is a morphism of smooth varieties, there is not in general an induced map on cousin complexes, so computing pullbacks of cohomology classes is difficult. In this talk I will explain how such pullbacks may nonetheless be computed, at least up to choosing a good enough cycle representing the cohomology class (which is always possible in principle, but may be difficult in practice). Time permitting, I will mention applications to the