Havet–Thomassé conjecture for trees with few leaves

Let $T$ be an oriented tree with $k$ edges and $ll$ leaves, and let a tournament be an orientation of a complete graph. Havet–Thomassé's conjecture. Every tournament on $k+\ell$ vertices contains a copy of $T$. The bound is motivated by the sharper behavior of paths and trees with few leaves; later results give near-linear bounds, but the stated bound is not known in general.