  The random access problem for compressed strings is to build a data structure
that efficiently supports accessing the character in position $i$ of a string
given in compressed form. Given a grammar of size $n$ compressing a string of
size $N$, we present a data structure using $O(n\Delta \log_\Delta \frac N n
\log N)$ bits of space that supports accessing position $i$ in $O(\log_\Delta
N)$ time for $\Delta \leq \log^{O(1)} N$. The query time is optimal for
polynomially compressible strings, i.e., when $n=O(N^{1-\epsilon})$.
