  The following will be shown: Let $I$ be a $\sigma$-ideal on a Polish space
$X$ with the property that the associated forcing of $I^+$ Borel subsets
ordered by $\subseteq$ is a proper forcing. Let E be an analytic or coanalytic
equivalence relation on this Polish space with all equivalence classes Borel.
If sharps of certain sets exist, then there is an $I^+$ Borel subset $C$ of $X$
such that $E \upharpoonright C$ is a Borel equivalence relation.
