The Connor et al. v. Coleman, Judge, United States Court of Appeals, et al., 1978 case was a significant ruling by the U.S Supreme Court that dealt with issues related to judicial discretion and civil rights litigation. The plaintiffs in this case were Alabama state officials who sought an injunction against federal judges from hearing any further cases involving school desegregation in Alabama without first notifying the Attorney General of Alabama and giving him an opportunity to be heard on behalf of the State's interest in maintaining control over its public schools. The Supreme Court held that it had no jurisdiction to issue such an injunction because there was no statutory or constitutional provision authorizing it to do so. Furthermore, the court stated that even if it did have such authority, issuing such an order would violate principles of comity between federal courts and state governments as well as infringe upon judicial independence by interfering with federal judges' ability to manage their dockets effectively.

In the dissenting opinion for Connor et al. v. Coleman, Judge, United States Court of Appeals, et al., Justice William Brennan disagreed with the majority's decision to dismiss a challenge against Mississippi's judicial election system on procedural grounds. He argued that the case raised significant constitutional questions about whether at-large elections diluted minority voting power and violated equal protection rights under the Fourteenth Amendment. Brennan believed these issues deserved full consideration by lower courts before reaching Supreme Court review rather than being dismissed prematurely due to technicalities in jurisdictional rules or standing requirements. In his view, dismissing such an important civil rights case without fully addressing its merits undermined public confidence in judiciary fairness and equality.