  Koutras has proposed some methods to construct reducible proper conformal
Killing tensors and Killing tensors (which are, in general, irreducible) when a
pair of orthogonal conformal Killing vectors exist in a given space. We give
the completely general result demonstrating that this severe restriction of
orthogonality is unnecessary. In addition we correct and extend some results
concerning Killing tensors constructed from a single conformal Killing vector.
A number of examples demonstrate how it is possible to construct a much larger
class of reducible proper conformal Killing tensors and Killing tensors than
permitted by the Koutras algorithms. In particular, by showing that all
conformal Killing tensors are reducible in conformally flat spaces, we have a
method of constructing all conformal Killing tensors (including all the Killing
tensors which will in general be irreducible) of conformally flat spaces using
their conformal Killing vectors.
