I present a formal model illustrating how institutions that constrain trial judges’ influence over legal cases have important, under-appreciated downsides. The model provides three novel insights. First, an unbiased trial judge makes judgments that are systematically biased in favor of powerful litigants. This results from their strategic anticipation of litigant appeals, and it allows them to put less effort into resolving cases. Second, when unbiased judges are assigned randomly to cases, they will produce more errors than a case assignment system allowing trial judges more freedom to select cases. This has implications for judicial selection: diversity on the bench may promote high quality decision-making under flexible case assignment procedures, but not under random case assignment. Third, even when a trial judge is explicitly biased in favor of a litigant, they will often (but not always) make fewer errors in their decision-making than an unbiased judge.