Abstract: The socially desirable design of the appeals process is analyzed assuming that it may involve either an initial discretionary review proceeding—under which the appeals court would decide whether to hear an appeal—or else a direct appeal. Using a stylized model, I explain that the appeals process should not be employed when the appellant’s initial likelihood of success falls below a threshold, that discretionary review should be used when the likelihood of success lies in a midrange, and that direct appeal should be sought when this likelihood is higher. Further, I emphasize that appellants should often be able to choose between discretionary review and direct appeal, notably because appellants may elect discretionary review to save themselves (and thus the judicial system) expense. This suggests the desirability of a major reform of our appeals process: appellants should be granted the right of discretionary review along with the right that they now possess of direct appeal at the first level of appeals.