We introduce in this article a class of transient random walks in a
random environment on $\mathbb{Z}^d$. When $d\ge 2$, these walks are ballistic
and we derive a law of large numbers, a central limit theorem and
large-deviation estimates. In the so-called nestling situation, large
deviations in the neighborhood of the segment $[0, v]$, $v$ being the limiting
velocity, are critical. They are of special interest in view of their close
connection with the presence of traps in the medium, that is, pockets where a
certain spectral parameter takes atypically low values.