The U.S. Supreme Court made big news Monday. As expected, in the next term it will hear Whitford v. Gill, a case challenging partisan gerrymandering in Wisconsin. Law professors and political operatives alike are in a tizzy. The Justices have a rare opportunity to significantly improve the way American elections work, by curbing the manipulations that deprive voters of an effective voice. It could have massive electoral consequences.

Gerrymandering is a hoary part of the American political system. Politicians have gleefully drawn electoral maps to benefit themselves and their parties since political bosses wore powdered wigs. The quirky phrase itself was coined to describe a district, signed into law by Massachusetts Governor Elbridge Gerry in 1812, that looked like a salamander.

But in recent years, the charm has worn off. In the past, creative if mischievous mapmaking was seen, in the proud words of one congressman, as a form of “modern art.” Now Big Data, computers and unified party control of statehouses at key moments have led to gerrymanders far more potent than their precursors. Politicians have learned to carve districts with ever-greater precision. Because they swept the 2010 midterms, Republicans have benefitted greatly from this.

A recent study by the Brennan Center shows the impact of these “extreme maps.” In Pennsylvania, for example, Donald Trump narrowly won in 2016, and Democrats won many statewide races in 2014. But 13 out of 18 congressional seats are held by Republicans. In narrowly divided North Carolina, with a Democratic governor and closely fought elections, Republicans have a 10-3 advantage in House seats. This kind of tilt is not found everywhere. In fact, seven states account for the worst gerrymandering. All told, that gives 16 or 17 seats to Republicans in Congress—a big chunk of the 24 seats Democrats would need to gain to win a majority.

The U.S. Supreme Court has watched this phenomenon warily, wincing but failing to act. The Justices don’t like gerrymandering. They have long been skeptical of the grubby ways politicians entrench themselves. But they felt, as Justice Anthony Kennedy wrote in the 2004 Veith case, that there were no “clear, manageable, and politically neutral standards” to guide their actions. How much gerrymandering is too much? Since then, however, maps became so extreme that a fresh set of legal challenges seemed ripe for the bringing. An armada of lawsuits moved through the federal courts. The most significant was the case in Wisconsin. There, a federal three-judge panel found that the entire state’s map was too imbalanced, “an unconstitutional political gerrymander” drawn to benefit the Republican Party. This was the first time in decades, if ever, that a federal court ruled this way.

Now, the Supreme Court will have its say. It’s a high-stakes legal battle. The good government challenge to the Wisconsin maps will be defended by Paul Smith, a legendary litigator who argued the landmark gay rights case Lawrence v. Texas. As with all big constitutional cases, the Court will likely receive friend of the court briefs from across the spectrum. These often matter greatly.

As with so much else at the high court, observers believe the case may turn on the views of Justice Kennedy. How to read the tea leaves? Kennedy has made clear his distaste for gerrymandering. In 2014, he joined an opinion upholding state redistricting reform that lustily denounced the practice. Yet he recently signed on to a dissent in another gerrymandering case, which implied that at least some partisan gerrymanders might be constitutionally permitted.

The lawyers have much to chew on. On Monday the Court also issued a “stay” of the appeals court’s order to Wisconsin to begin drawing its maps. An ominous sign that five justices including Kennedy disagree with the appellate court? Or merely a recognition that this is a big issue where the high court will ultimately have the final say? Speculation can be maddening, and ultimately unproductive. On this case, as on few others, the facts and consequences of the rulings will matter most. Some justices might insist that the Court can’t do anything here without a precise rule. Others will want to make sure that a ruling in one egregious situation does not let loose a torrent of new cases for them to then decide.

This comes at a time of increasing public awareness of the broken political system, with rising demands for change. In Michigan, activists are readying a ballot initiative to create a nonpartisan commission to draw district lines. Ohio Governor John Kasich already backed a successful effort to reform legislative redistricting, and looks ready to support one for federal races as well. California and Arizona already have commissions, created by voters through ballot measures. In Florida, a constitutional amendment prohibited partisan gerrymandering, giving judges the power to stop it—with some promising results, too. Reform is in the air.

But for now, the august Supreme Court chamber will be the main stage. Historically the justices have shrunk from cases with major political implications. But at times the Court speaks loudly ad powerfully when it comes to democracy. In the 1960s, it thundered that our system depended on “one person, one vote,” meaning roughly equal legislative districts. More recently, and much more destructively, the justices shredded campaign finance law in Citizens United, and gravely weakened the Voting Rights Act in Shelby County v. Holder.

This case offers a rare chance for a vital constitutional advance when it comes to meaningful voting rights. Citizens know the system is broken. In the last midterm election, turnout scraped near the lowest level in 72 years. Far too many places lack genuine competition. A map of deep red and blue districts yields a polarized Congress. When political manipulation goes too far, the Court has a chance to say: it’s too much. All eyes will be on the high court starting the first Monday in October. Its ruling – presumably by June 2018 – will rattle ballot boxes around the country.