For most of the last century, the Supreme Court has operated under an unwritten rule of four — the agreement of four of the nine justices is needed before the Court consents to docket and rule on a new case.

On Tuesday, the Court appeared to signal that a higher hurdle — a rule of five — is required before the justices will hear oral arguments in a new breed of habeas corpus petition filed by death row inmates directly to the Supreme Court. The shift could make it substantially harder for condemned prisoners to bring constitutional claims to the Court’s attention.