Frankfurter demanded that the opinion in "Brown II" (1955) order schools to desegregate with "all deliberate speed". Some school boards used this phrase as an excuse to defy the demands of the first Brown decision. For fifteen years, schools in many states of the South remained segregated; in some cases systems closed their schools, and new private schools were opened by white parents for their children. In "Alexander v. Holmes County Board of Education", the Court wrote, "The obligation of every school district is to terminate dual school systems at once and to operate now and hereafter only unitary schools." Frankfurter's "all deliberate speed" formula was intended to constrain the federal judiciary toward a gradualist approach to school integration, but his formula backfired. By divorcing the plaintiff's injury from the remedy afforded, "Brown II" gave birth to modern Public Law Litigation, which today affords federal courts broad power to reform state institutions.