  We consider Bel-Robinson-like higher derivative conserved two-index tensors
$H_\mn$ in simple matter models, following a recently suggested Maxwell field
version. In flat space, we show that they are essentially equivalent to the
true stress-tensors. In curved Ricci-flat backgrounds it is possible to
redefine $H_\mn$ so as to overcome non-commutativity of covariant derivatives,
and maintain conservation, but they become model- and dimension- dependent, and
generally lose their simple "BR" form.
