GUANTANAMO DETAINEES: The court is being asked to determine whether detainees at the Guantanamo Bay naval base can use U.S. civilian courts to challenge their indefinite imprisonment after Congress passed and President Bush signed a law that says they cannot. (Boumediene v. Bush, 06-1195, Al-Odah v. U.S., 06-1196).

CRACK-POWDER COCAINE DISPARITY: At issue is whether a federal judge has the discretion to impose a more lenient sentence on sellers of crack cocaine, most of whom are black, departing from federal sentencing guidelines that call for significantly longer prison terms for sellers of crack than for sellers of powder cocaine. Tuesday. (Kimbrough v. U.S., 06-6330).

LETHAL INJECTIONS: Death row inmates claim that lethal injection as practiced in Kentucky violates the Constitution's ban on cruel and unusual punishment. (Baze v. Rees, 07-5439).

VOTER ID: Democrats and civil rights groups say laws requiring voters to produce photo identification in order to cast a ballot violate the Constitution. (Crawford v. Marion County Election Board, 07-21, Indiana Democratic Party v. Rokita, 07-25).

CHILD PORNOGRAPHY: The government's appeal of an appeals court ruling declaring unconstitutional a portion of the child pornography law that criminalizes an individual's promotion of child porn, whether or not he actually possesses it. The part of the law making it a crime to have child porn is not at issue. Oct. 30. (U.S. v. Williams, 06-694).

PRESIDENTIAL POWER: The Bush administration is taking the side of a Mexican national who is on death row in Texas in a case that probes the president's power to set aside a state law that conflicts with an international treaty. Oct. 10. (Medellin v. Texas, 06-984).

INVESTOR LAWSUITS: Whether third parties such as investment banks, accountants, lawyers or vendors can be found liable in shareholder lawsuits for scheming with companies accused of deceiving investors, a case that could determine the outcome of other investor lawsuits including one stemming from the Enron scandal. Oct. 9. (Stoneridge Investment v. Scientific-Atlanta, 06-43).

LOUISIANA DEATH CASE: A black man convicted of killing his wife's companion and sentenced to death by an all-white jury in Louisiana says he did not get a fair trial because the prosecutor improperly dismissed prospective black jurors and compared the defendant with O.J. Simpson, who had recently been acquitted of killing his wife and another man. (Snyder v. Louisiana, 06-10119).

GOVERNMENT BONDS: May a state tax the interest on municipal bonds from outside the state while exempting residents from tax on in-state bonds, a case with enormous implications for the municipal bond market if the court affirms a Kentucky court ruling that the practice is unconstitutional. Nov. 5. (Department of Revenue of Kentucky v. Davis, 06-666).

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Some major cases the court could decide to hear this term:

D.C. GUN BAN: Both sides want the court to take the appeal of a lower court ruling striking down Washington, D.C.'s ban on handguns as a violation of the Second Amendment. (District of Columbia v. Heller, 07-290).

EXECUTION OF CHILD RAPIST: A Louisiana man is the only person in the country on death row for rape, in this case the sexual assault of his 8-year-old stepdaughter. (Kennedy v. Louisiana, 07-343).