  We consider a Zipf--Poisson ensemble in which $X_i\sim\poi(Ni^{-\alpha})$ for
$\alpha>1$ and $N>0$ and integers $i\ge 1$. As $N\to\infty$ the first $n'(N)$
random variables have their proper order $X_1>X_2>...>X_{n'}$ relative to each
other, with probability tending to 1 for $n'$ up to
$(AN/\log(N))^{1/(\alpha+2)}$ for an explicit constant $A(\alpha)\ge 3/4$. The
rate $N^{1/(\alpha+2)}$ cannot be achieved. The ordering of the first $n'(N)$
entities does not preclude $X_m>X_{n'}$ for some interloping $m>n'$. The first
$n"$ random variables are correctly ordered exclusive of any interlopers, with
probability tending to 1 if $n"\le (BN/\log(N))^{1/(\alpha+2)}$ for $B<A$. For
a Zipf--Poisson model of the British National Corpus, which has a total word
count of $100{,}000{,}000$, our result estimates that the 72 words with the
highest counts are properly ordered.
