The Supreme Court imposed new limits Monday on states trying to restrain the influence of money in politics, striking down a law that tied the amount of public funds a candidate receives to how much privately funded rivals spend.

The 5-4 ruling was the latest in a series of decisions by the court’s conservative majority upending campaign finance laws. But the court did not attack the validity of using public funds for campaign financing, giving a glimmer of hope to advocates of restrictions on spending in political campaigns.

Instead, Chief Justice John Roberts’ majority opinion dwelled on the so-called trigger mechanism in an Arizona law that provided differing levels of money to publicly funded candidates based on the spending by privately funded rivals and independent groups.

The law was passed after a public corruption scandal and was intended to reward candidates who forgo raising their own campaign cash, even in the face of heavy spending by opponents with private money. Those who challenged the Arizona law said it caused them to rein in spending to prevent their political opponents from getting a fresh infusion of state money.

The court said the trigger violates the First Amendment, but left in place the rest of Arizona’s public financing system.

“Laws like Arizona’s matching funds provision that inhibit robust and wide-open political debate without sufficient justification cannot stand,” Roberts said.

At least four other states, Maine, New Mexico, North Carolina and Wisconsin, have similar “trigger” provisions that affect some political races, and could be vulnerable.