  The Directed Grid Theorem, stating that there is a function $f$ such that a
directed graphs of directed treewidth at least $f(k)$ contains a directed grid
of size at least $k$ as a butterfly minor, after being a conjecture for nearly
20 years, has been proven in 2015 by Kawarabayashi and Kreutzer. However, the
function $f$ obtained in the proof is very fast growing.
  In this work, we show that if one relaxes directed grid to bramble of
constant congestion, one can obtain a polynomial bound. More precisely, we show
that for every $k \geq 1$ there exists $t = \mathcal{O}(k^{48} \log^{13} k)$
such that every directed graph of directed treewidth at least $t$ contains a
bramble of congestion at most $8$ and size at least $k$.
