In the case of Mississippi v. Arkansas in 1974, the Supreme Court was asked to resolve a dispute over the boundary line between these two states. The controversy arose due to changes in the course of the Mississippi River, which serves as part of their border. According to common law principles and previous court decisions, when a river serving as a boundary shifts gradually through natural processes (a process called accretion), state borders shift with it; but if it jumps its banks suddenly (avulsion), they do not change. In this case, both sides agreed that an avulsive event had occurred around Island No. 76 causing significant movement of water from one side to another but disagreed on whether or not this changed their shared border. The Supreme Court held that despite substantial alterations caused by human intervention such as dredging and dike-building along with natural forces leading up to avulsion at Island No. 76, there was no evidence showing that main channel had moved away from its former bed permanently enough for Arkansas' claim over new territory based on doctrine of accretion could be justified under existing legal standards governing interstate boundaries disputes involving navigable rivers like Mississippi River.

The dissenting opinion in the case of Mississippi v. Arkansas, 1974, argued that the majority's decision to deny Mississippi's motion for leave to file a bill of complaint was incorrect. The dissenters believed that this denial prevented Mississippi from asserting its rights over an area known as "Mile Point Cut-Off." They contended that there were substantial questions about whether or not Mile Point Cut-Off had been artificially created and if it should be considered part of the main channel of the river. These issues, they felt, warranted further investigation and adjudication by a special master rather than outright dismissal by the court. Furthermore, they expressed concern about potential implications on future interstate disputes involving similar circumstances.