Washington ? The first major abortion case since Chief Justice John Roberts Jr. joined the court last month comes before the justices next week, and even though it could be anticlimactic in the end, both sides in the debate view it as a warm-up for even more consequential cases ahead.

The case is Ayotte v. Planned Parenthood. If the court divides 5 to 4 with Justice Sandra Day O’Connor in the majority but cannot produce a decision before O’Connor is replaced, then the court will have to redo the case in its next term.

But if not, “it could be a vehicle to revolutionize abortion law if they want to use it,” said David Garrow, a Supreme Court historian and specialist on abortion law at Britain’s Cambridge University.

The case stems from a 2003 New Hampshire law requiring teenagers to tell a parent before getting an abortion. While the law has an exception for girls who would die without the procedure, New Hampshire lawmakers omitted an exception for other non-life-threatening health problems because they felt it would render the law meaningless.

The new law has never been enforced, because two federal courts have said the lack of a health exception made it unconstitutional.

The Bush administration supports the New Hampshire law, telling the court in a friend-of-the-court brief that the case “may have direct relevance” to its defense of the federal law banning the late-term procedure that its opponents refer to as “partial-birth abortion” – a law that has been struck down by lower federal courts in rulings that the administration has asked the Supreme Court to overturn.

At the heart of the matter is a relatively arcane issue having to do not with whether the law is unconstitutional but with how the court goes about deciding it is unconstitutional.

In 1987, in a non-abortion case, the court ruled that a law could only be struck down “on its face” – that is, before it goes into effect – if there is no possible constitutional way to enforce it.

But in a landmark 1992 abortion ruling, Planned Parenthood v. Casey, the court seemed to apply a different standard to state abortion regulations, noting that such rules would run afoul of the constitution if they posed an “undue burden” to women in “a large fraction of cases.”

Parental involvement laws regarding abortion are politically popular. All but six states have some form of statute that says girls younger than 18 must involve at least one parent or guardian in the decision to terminate a pregnancy.