  Let $M$ be a compact closed manifold of variable negative curvature. Fix an
element $\operatorname{id} \neq \gamma$ in the fundamental group $\Gamma$ of
$M$, and denote the set of elements in $\Gamma$ that are conjugate to $\gamma$
by $\operatorname{Conj}_\gamma$. For two points $x, y$ in the universal cover
of $M$, we obtain asymptotics for the number of
$\operatorname{Conj}_\gamma$--orbits of $y$ that lie in a ball of radius $T$
centered at $x$, as $T$ tends to infinity. If $M$ is two-dimensional, or of
dimension $n \geq 3$ and curvature bounded above by $-1$ and below by
$-(\frac{n-1}{n-2})^2$, we find an exponentially small error term for this
count.
