  We consider a nearest-neighbor, one-dimensional random walk $\{X_n\}_{n\geq
0}$ in a random i.i.d. environment, in the regime where the walk is transient
with speed v_P > 0 and there exists an $s\in(1,2)$ such that the annealed law
of $n^{-1/s} (X_n - n v_P)$ converges to a stable law of parameter s. Under the
quenched law (i.e., conditioned on the environment), we show that no limit laws
are possible. In particular we show that there exist sequences {t_k} and {t_k'}
depending on the environment only, such that a quenched central limit theorem
holds along the subsequence t_k, but the quenched limiting distribution along
the subsequence t_k' is a centered reverse exponential distribution. This
complements the results of a recent paper of Peterson and Zeitouni
(arXiv:0704.1778v1 [math.PR]) which handled the case when the parameter
$s\in(0,1)$.
