  We prove the generalised Tate conjecture for H^3 of products of elliptic
curves over finite fields, by slightly modifying an argument of M. Spiess
concerning the Tate conjecture. We prove it fully if the elliptic curves run
among at most 3 isogeny classes. We also show how things become more intricate
from H^4 onwards, for more that 3 isogeny classes.
