  We consider random walks in strong-mixing random Gibbsian environments in
$\mathbb{Z}^d, d\ge 2$. Based on regeneration arguments, we will first provide
an alternative proof of Rassoul-Agha's conditional law of large numbers (CLLN)
for mixing environment Rassoul-Agha (2005). Then, using coupling techniques, we
show that there is at most one nonzero limiting velocity in high dimensions
($d\ge 5$).
