Non-precedent decisions are the norm in federal appellate courts, and are seen by judges as a practical necessity given the size of their dockets. Yet the system has always been plagued by doubts. If only some decisions are designated to be precedents, questions arise about whether courts might be acting arbitrarily in other cases. Such doubts have been overcome in part because nominally unpublished decisions are available through standard legal research databases. This creates the appearance of transparency, mitigating concerns that courts may be acting arbitrarily. But what if this appearance is an illusion? This Article reports empirical data drawn from a study of immigration appeals showing that many – and in a few circuits, most – decisions by the federal courts of appeals are in fact unavailable and essentially invisible to the public. The Article reviews the reasons why non-publication is a practical, constitutional and philosophical challenge for judges. It argues that the existence of widespread invisible adjudication calls for a re-thinking of the way courts operate and the way scholars study them.