  Examples of "enhanced ultraviolet cancellations" with no known
standard-symmetry explanation have been found in a variety of supergravity
theories. By examining one- and two-loop examples in four- and five-dimensional
half-maximal supergravity, we argue that enhanced cancellations in general
cannot be exhibited prior to integration. In light of this, we explore
reorganizations of integrands into parts that are manifestly finite and parts
that have poor power counting but integrate to zero due to integral identities.
At two loops we find that in the large loop-momentum limit the required
integral identities follow from Lorentz and SL(2) relabeling symmetry. We carry
out a nontrivial check at four loops showing that the identities generated in
this way are a complete set. We propose that at $L$ loops the combination of
Lorentz and SL($L$) symmetry is sufficient for displaying enhanced
cancellations when they happen, whenever the theory is known to be ultraviolet
finite up to $(L-1)$ loops.
