  For a fixed cusp form $\pi$ on $\operatorname{GL}_3(\mathbb{Z})$ and a
varying Dirichlet character $\chi$ of prime conductor $q$, we prove that the
subconvex bound \[ L(\pi \otimes \chi, \tfrac{1}{2}) \ll q^{3/4 - \delta} \]
holds for any $\delta < 1/36$. This improves upon the earlier bounds $\delta <
1/1612$ and $\delta < 1/308$ obtained by Munshi using his $\operatorname{GL}_2$
variant of the $\delta$-method. The method developed here is more direct. We
first express $\chi$ as the degenerate zero-frequency contribution of a
carefully chosen summation formula \`a la Poisson. After an elementary
"amplification" step exploiting the multiplicativity of $\chi$, we then apply a
sequence of standard manipulations (reciprocity, Voronoi, Cauchy--Schwarz and
the Weil bound) to bound the contributions of the nonzero frequencies and of
the dual side of that formula.
