  We show that the ambiguity of Murre's Chow-Kuenneth projector for degree 1
has certain good properties, assuming only that it factors through a Chow
motive of a smooth irreducible curve. This is compatible with a picture
obtained by using Beilinson's conjectural mixed motives, and implies for
instance the independence of the Chow motive defined by the middle
Chow-Kuenneth projector for surfaces.
