  We diagonalize Q-operators for rational homogeneous sl(2)-invariant
Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the
fundamental commutation relations relevant for this case from the Yang-Baxter
equation we demonstrate that the Q-operators act diagonally on the Bethe
vectors if the Bethe equations are satisfied. In this way we provide a direct
proof that the eigenvalues of the Q-operators studied here are given by
Baxter's Q-functions.
