IN HER first argument before the Supreme Court—20 years before Bill Clinton would nominate her to be America’s 107th justice—Ruth Bader Ginsburg asked nine men to put themselves into the shoes of an air-force lieutenant who had been treated differently because she was a woman. In 1973, Sharron Frontiero challenged a rule giving male airmen automatic housing benefits for their wives while women could do the same only by proving their husbands were dependent on them. It was, as directors Betsy West and Julie Cohen show in “RBG”, an informative and affecting documentary film, a significant step toward persuading the justices that America’s constitution has something to say about women’s rights.

Lawyers addressing the Supreme Court these days rarely get more than a few sentences out before they are lashed with questions from the bench. The colloquy wasn’t always that heated in the 1970s, but it was rare for a lawyer to speak for minutes on end without being questioned. In Ms Ginsburg’s inaugural trip to the lectern for Frontiero v Richardson, she spoke more than 1,200 words, in nearly 11 minutes, without a single interruption. “At the time, I wondered, are they just indulging me, and not listening?” Justice Ginsburg recalls in the film. “Or am I telling them something they haven’t heard before—and are they paying attention?”

It seems that they were paying attention: Ms Frontiero won an 8-1 decision. “A person’s sex bears no necessary relationship to ability”, Ms Ginsburg had told the justices in her monologue. “Women today face discrimination in employment as pervasive and more subtle than discrimination encountered by minority groups”, and discriminatory rules “help keep woman in her place, a place inferior to that occupied by men in our society”. Justice William Brennan’s opinion drew liberally from these themes. America “has had a long and unfortunate history of sex discrimination”, he wrote, which “put women not on a pedestal, but in a cage”. In the 1970s, he continued, “women still face pervasive”, if “subtle...discrimination”.

Despite giving Ms Frontiero and other women an equal shot at workplace benefits, Frontiero did not deliver the full victory Ms Ginsburg and her colleagues sought. In a brief she filed for the American Civil Liberties Union and in her oral advocacy, Ms Ginsburg asked the justices to declare gender a “suspect classification”: an identity marker akin to race, triggering especially rigorous review when the government uses it to treat people differently. Justice Brennan was ready to give gender this constitutional status, as were three of his brethren; but the Supreme Court cannot do anything without five votes, and the other four justices siding with Ms Frontiero and her husband declined to go that far.

Hoping the court would guarantee stronger protections against gender discrimination, Ms Ginsburg pressed on, arguing five more gender-equality cases before the court in the coming years and winning four. A turning point unexplored in "RBG" came in 1976, when Ms Ginsburg helped develop the legal strategy for Craig v Boren, a case brought by a freshman at Oklahoma State University. The young man took issue with an Oklahoma law that permitted 18-year-old women to buy 3.2%-alcohol beer—a brew considered “nonintoxicating” and dubbed “near beer”—while delaying this honour for men until their 21st birthdays. The justices found the law to be based on “loose-fitting generalities concerning the drinking tendencies” of young men and women and were not impressed by a study finding that while only 0.18% of females aged 18-20 were arrested for drunk driving, 2% of men were. Most notably, for the first time, a majority of the court elevated gender above the lowest level of review. Heeding a suggestion in Ms Ginsburg’s brief that gender may merit "something in between" mere rational-basis review and strict scrutiny, the Craig court established a new test: “intermediate scrutiny”, a Goldilocks approach to judging the constitutionality of gender-based distinctions that is demanding but not quite as strict as when the law discriminates according to race.

It is perhaps telling that an institution populated exclusively by men for nearly two centuries—the first woman, Sandra Day O’Connor, took her chair in 1981—chose a young man in search of beer as the plaintiff whose plight would spur the justices to take gender discrimination more seriously. But showing that gender discrimination hurts men and women alike was part of Ms Ginsburg’s plan. In what biographer and law professor Wendy Williams calls Ms Ginsburg’s favourite case, Weinberger v Wiesenfeld, Ms Ginsburg defended a widowed man’s right to Social Security payments for child care that had been reserved for women whose husbands had died. She won a unanimous judgment.

By appealing to the justices’ sense of fairness and presenting them with sympathetic male and female plaintiffs, Ms Ginsburg built America’s gender equality standards brick by brick. Her patient strategy has also laid a foundation for cutting-edge advances in civil liberties and civil rights for LGBT Americans. In the past year and a half, two circuit courts have ruled that discrimination against gays and lesbians is a form of gender discrimination under Title VII of the Civil Rights Act of 1964. And the court’s marriage equality decision in 2015, while falling short of explicitly giving gays and lesbians heightened scrutiny, “effectively establishes” that sexual orientation constitutes a suspect classification, according to Gary Buseck of Gay and Lesbian Advocates and Defenders (GLAD).

“RBG” reveals a lot about the jurist known as the Notorious RBG for her fierce dissents from conservative rulings on so-called "partial-birth" abortion, contraceptive care, campaign finance and voting rights. We see Justice Ginsburg planking with her personal trainer, riding an elephant with her late friend and jurisprudential nemesis Antonin Scalia, moved to tears at the opera, and erupting in stitches when seeing herself parodied on “Saturday Night Live”. But what the film does best is to show the quieter parts of this remarkable justice's life. Her loving, decades-long relationship with Marty Ginsburg, a talented lawyer who died in 2010, and the equality and mutuality of their marriage, went hand-in-hand with her mission to earn women a measure of respect and autonomy in America.