  We consider electromagnetic finite-volume effects through order $1/L^3$ in
different formulations of QED, where $L$ is the periodicity of the spatial
volume. An inherent problem at this order is the appearance of
structure-dependent quantities related to form factors and the analytical
structure of the correlation functions. The non-local constraint of the widely
used QED$_{\textrm{L}}$ regularization gives rise to structure-dependent
effects that are difficult to evaluate analytically and can act as a precision
bottleneck in lattice calculations. For this reason, we consider general volume
expansions relevant for the mass spectrum as well as leptonic decay rates in
QED$_{\textrm{C}}$, QED$_{\textrm{L}}$ and QED$_{\textrm{L}}^{\textrm{IR}}$,
the latter being a class of non-local formulations generalising
QED$_{\textrm{L}}$. One choice within this class is QED$_{\textrm{r}}$, first
introduced at this conference, and we show that the effects of non-locality for
the $1/L^3$ term in the expansion can be removed. We observe that there are
still $1/L^3$ contributions unrelated to the (non-)locality of the studied QED
formulations, but rather to collinear singularities in the physical amplitudes.
