  We consider a one-dimensional transient cookie random walk. It is known from
a previous paper that a cookie random walk $(X_n)$ has positive or zero speed
according to some positive parameter $\alpha >1$ or $\le 1$. In this article,
we give the exact rate of growth of $(X_n)$ in the zero speed regime, namely:
for $0<\alpha <1$, $X_n/n^{\frac{\alpha+1}{2}}$ converges in law to a
Mittag-Leffler distribution whereas for $\alpha=1$, $X_n(\log n)/n$ converges
in probability to some positive constant.
