Wilson-like Dirac operators can be written in the form $D=\gamma_\mu\nabla_\mu-\frac {ar}{2} \Delta$. For Wilson fermions the
standard two-point derivative $\nabla_\mu^{(\mathrm{std})}$ and 9-point Laplacian $\Delta^{(\mathrm{std})}$ are used. For
Brillouin fermions these are replaced by improved discretizations $\nabla_\mu^{(\mathrm{iso})}$ and $\Delta^{(\mathrm{bri})}$
which have 54- and 81-point stencils respectively. We derive the Feynman rules in lattice perturbation theory for the Brillouin
action and apply them to the calculation of the improvement coefficient $\csw$, which, similar to the Wilson case, has a
perturbative expansion of the form $\csw=1+\csw^{(1)}g_0^2+\mathcal{O}(g_0^4)$. For $N_c=3$
we find ${\csw}^{(1)}_\text{Brillouin} =0.12362580(1) $, compared to ${\csw}^{(1)}_\text{Wilson} = 0.26858825(1)$, both for $r=1$.