  This paper has two main results, which are connected through the fact that
the first is a key ingredient in the second. Both are extensions of results
concerning directional transience of nearest-neighbor random walks in random
environments to allow for bounded jumps. Zerner and Merkl proved a 0-1 law for
directional transience for planar random walks in random environments. We
extend the result to non-planar i.i.d. random walks in random environments on
$\mathbb{Z}^2$ with bounded jumps. Sabot and Tournier characterized directional
transience for a given direction for nearest-neighbor random walks in Dirichlet
environments on $\mathbb{Z}^d$, $d\geq1$. We extend this characterization to
random walks in Dirichlet environments with bounded jumps.
