States may not demand proof of citizenship from people registering to vote, the Supreme Court ruled by a decisive 7-2 today.

The majority signaled it would also be ready to strike down any requirement tougher than what’s set out in the 1993 federal “motor voter” law, which was designed by Congress to simplify registration.

The decision, and the language behind it, is therefore a significant victory for mainstream Democrats, who want to expand access to the polls in part because they’re confident they’ll win most of the new voters. And it’s a defeat for mainstream Republicans, who express intense concern about the potential for election fraud but also know that polls show them doing poorly among groups underrepresented on the rolls — ethnic minorities, immigrants and older people.

The case was the most newsworthy of the five announced today. The court next convenes on Thursday. It has 14 more decisions to reveal before adjourning for the summer, including potential landmark rulings about gay marriage, affirmative action and the year’s much more significant voting rights case: whether states with histories of racial discrimination should have to get federal permission before drawing new political boundaries or implementing other changes to their elections.

But this morning’s majority opinion, by Justice Antonin Scalia, offered few clues about how the court might address the constitutionality of the Voting Rights Act.

What the court struck down today was a law enacted eight years ago in Arizona by voter referendum, known as Proposition 200, requiring would-be voters to offer physical proof of citizenship as a condition of registration. The federal law requires only a signature on a postcard stipulating, under penalty of perjury, that the registrant is a citizen.

The issue was whether a state could set documentation requirements tougher than those set out by the federal government. The court said it couldn’t, at least not before seeking congressional permission for an exception and then returning to court if it didn’t get its way. (Justices Clarence Thomas and Samuel A. Alito Jr. were the dissenters.)

Alabama, Georgia, Kansas and Tennessee have requirements similar to Arizona’s, and a dozen other states have been debating legislation to add new registration requirements. (About 30 states have laws requiring proof of identification before casting a vote, which weren’t an issue in today’s case.)

The decision also comes as the Senate resumes debate on an immigration overhaul bill that would provide a path to citizenship for illegal immigrants while bolstering border security. An interest in preventing non-citizen Latino’s from voting was what sparked support for the Arizona referendum, but figures used in the legal challenge suggested the effect was different: Of the 31,000 potentially legal voters in Arizona blocked from registering in the first 20 months the law was on the books, 1 in 5 was Hispanic.