  Let $\bfG$ be a connected reductive algebraic group defined over $\F_q$,
where $q$ is a power of a prime $p$ that is good for $\bfG$. Let $F$ be the
Frobenius morphism associated with the $\FF_q$-structure on $\bfG$ and set $G =
\bfG^F$, the fixed point subgroup of $F$. Let $\bfP$ be an $F$-stable parabolic
subgroup of $\bfG$ and let $\bfU$ be the unipotent radical of $\bfP$; set $P =
\bfP^F$ and $U = \bfU^F$. Let $G_\uni$ be the set of unipotent elements in $G$.
In this note we show that the number of conjugacy classes of $U$ in $G_\uni$ is
given by a polynomial in $q$ with integer coefficients.
