The U.S. Supreme Court’s strengthened conservative majority made its first move toward giving states more power to regulate abortion, as the justices upheld an Indiana law requiring clinics to bury or cremate fetal remains.

The justices ruled Tuesday that a federal appeals court was wrong to strike down the measure as unconstitutional. Only two justices — Ruth Bader Ginsburg and Sonia Sotomayor — indicated publicly that they disagreed with the ruling. The court ruled without hearing arguments in the case.

The three-page opinion, issued by the court as a whole, said the state has a legitimate interest in ensuring the proper disposal of fetal remains. The court said opponents never argued that the measure put an unconstitutional “undue burden” on a woman’s right to obtain an abortion.

“This case, as litigated, therefore does not implicate our cases applying the undue burden test to abortion regulations,” the court said.

In a dissenting opinion, Ginsburg said the case “implicates the right of a woman to choose to have an abortion before viability and to obtain it without undue interference from the state.”

The Supreme Court also said it won’t hear Indiana’s effort to revive a separate provision that would bar abortions based on the fetus’s race or gender or the risk of a genetic disorder, such as Down syndrome.

Indiana argued that its law on disposal of fetal remains is consistent with the Supreme Court’s 1992 Planned Parenthood v. Casey decision, which upheld the fundamental right to abortion but said states have an interest in protecting fetal life after viability.

The measure applies only to abortion clinics and doesn’t bar a woman from disposing of the tissue herself. The law lets clinics cremate or bury fetuses from multiple abortions together.

Full story at Bloomberg News.