  We address a recent proposal concerning 'surplus structure' due to Nguyen et
al. ['Why Surplus Structure is Not Superfluous.' Br. J. Phi. Sci. Forthcoming.]
We argue that the sense of 'surplus structure' captured by their formal
criterion is importantly different from---and in a sense, opposite to---another
sense of 'surplus structure' used by philosophers. We argue that minimizing
structure in one sense is generally incompatible with minimizing structure in
the other sense. We then show how these distinctions bear on Nguyen et al.'s
arguments about Yang-Mills theory and on the hole argument.
