  Superspace power-counting rules give estimates for the loop order at which
divergences can first appear in non-renormalisable supersymmetric field
theories. In some cases these estimates can be improved if harmonic superspace,
rather than ordinary superspace, is used. The new estimates are in agreement
with recent results derived from unitarity calculations for maximally
supersymmetric Yang-Mills theories in five and six dimensions. For N=8
supergravity in four dimensions, we speculate that the onset of divergences may
correspondingly occur at the six loop order.
