  The hypothetical existence of a good theory of mixed motives predicts many
deep phenomena related to algebraic cycles. One of these, a generalization of
Bloch's conjecture says that "small Hodge diamonds" go with "small Chow
groups". Voisin's method (which produces examples with small Chow groups) is
analyzed carefully to widen its applicability. A threefold of general type
without 1- and 2-forms is exhibited for which this extension yields Bloch's
generalized conjecture.
