The Supreme Court returns to work Oct. 3 and will immediately confront some high-profile cases, among them:

ABORTION: The constitutionality of a New Hampshire parental notification law that lacks an emergency health exception for minors. Justices could use the case to make it harder for opponents to challenge abortion (search) restrictions.

PHYSICIAN-ASSISTED SUICIDE: The Bush administration's challenge to Oregon's law allowing physician-assisted suicide (search).

DEATH PENALTY: Four capital punishment cases, including one that will determine when prisoners can use DNA evidence to get a new trial.

DON'T ASK, DON'T TELL: A test of a law that requires colleges that get federal funding to allow military recruiters. Some law schools want to bar recruiters as a way of protesting the Pentagon's "don't ask, don't tell" policy (search) excluding openly gay people from military service.

RELIGIOUS FREEDOM: The Bush administration's appeal over a church's use of hallucinogenic tea in its religious services. The government contends the tea is illegal and potentially dangerous.

POLICE SEARCHES: Whether police may search a home when one occupant consents but another does not, without violating the Fourth Amendment ban against unreasonable searches and seizures.