  The following critical phenomenon was recently discovered. When a memoryless
source is compressed using a variable-length fixed-distortion code, the fastest
convergence rate of the (pointwise) compression ratio to the optimal $R(D)$
bits/symbol is either $O(\sqrt{n})$ or $O(\log n)$. We show it is always
$O(\sqrt{n})$, except for discrete, uniformly distributed sources.
