In the case of Mississippi v. Arkansas in 1973, the Supreme Court was asked to settle a dispute over state boundaries between Mississippi and Arkansas. The controversy arose due to changes in the course of the Mississippi River, which serves as a boundary between several states. According to principles established by previous cases, when a river serving as a boundary suddenly changes its course (avulsion), it does not affect state lines; however, if it gradually shifts its bed (accretion), then boundaries change accordingly. In this case, both states agreed that an avulsive event occurred but disagreed on whether subsequent accretion had also taken place - with each interpretation favoring one state's claim over certain territory. The court appointed Special Master Elbert Tuttle who found that there had been no significant accretion following the avulsion and thus recommended ruling in favor of Arkansas' claim. However, after reviewing evidence presented by both sides including historical maps and testimonies from geologists and engineers among others -the Supreme Court rejected these findings concluding instead that substantial accretion did occur post-avulsion thereby altering original boundary line. Therefore,the court ruled against Arkansas’ claims for sovereignty over lands lying eastwardly beyond said new main channel resulting from avulsive shift or jump made by waters of Mississippi River during flood period early in year 1937.

The dissenting opinion in the Mississippi v. Arkansas case argued that the majority's decision to deny Mississippi's motion for leave to file a bill of complaint against Arkansas was unjustified. The dissenters believed that there were significant unresolved issues related to boundary disputes between the two states, which warranted further examination and adjudication by the Supreme Court. They contended that this dispute over territorial boundaries should not be dismissed without proper consideration, as it involved important questions about state sovereignty and jurisdictional rights under federal law. Furthermore, they criticized the majority for failing to provide clear guidance on how such interstate conflicts should be resolved in future cases.