The Supreme Court refused on Tuesday to consider the rights of same-sex parents in a setback for two gay men who wanted both of their names listed on their adopted son's birth certificate.

In a case closely watched by gay rights advocates, the high court rejected without comment an appeal by Oren Adar and Mickey Ray Smith, who sued to be listed as parents on a Louisiana birth certificate of the infant they adopted.

The justices let stand a ruling by a U.S. appeals court that a Louisiana registrar's decision not to list both men does not violate the child's right to equal protection under the law and does not deny legal recognition of the New York adoption.

In Louisiana, adopted children can get new birth certificates with their new parents' names on them. In the state, only married couples may adopt a child.

Because the gay couple was not married, the registrar refused to list both names on the birth certificate but offered to put one name on because Louisiana also allows a single-parent adoption.

There have been a number of major legal battles over the rights of homosexuals, including a landmark gay marriage case from California and cases on the rights of gays to adopt.

The boy, identified in court documents only as J.C., was born in Shreveport, Louisiana, in 2005. His mother gave Adar and Smith custody of the baby shortly after birth and the couple legally adopted the infant in New York state in 2006.

After the adoption, Adar and Smith wanted the birth certificate changed with their names listed instead of the biological parents. The couple, former California residents, now live in the Orlando, Florida, area.

Washington-based attorney Paul Smith argued in the Supreme Court appeal that Louisiana unconstitutionally treated children differently based on the marital status of their adoptive parents. He also said the Constitution required states to accept as valid legal judgments issued in other states.

Louisiana Attorney General James Buddy Caldwell urged the Supreme Court to reject the appeal and said the appeal court's ruling does not merit review.

He said the high court should not confront the issues now, that society's views about the family were changing and the issues were likely to come up again in the future.

The Supreme Court case is Oren Adar v. Darlene Smith, No. 11-46.