This paper considers a game in which imperfectly informed jurors who differ in their thresholds of reasonable doubt must decide whether to convict or acquit a defendant. Jurors deliberate prior to voting on the fate of the defendant, and the defendant is convicted only if all jurors vote to convict. Although it has been established that full information revelation is impossible when jurors have sufficiently heterogeneous preferences, this paper demonstrates that if each juror shares preferences with a small fraction of the other jurors, it is possible to obtain enough information revelation so that the correct decision is made with probability arbitrarily close to one in large juries.