A side effect of those decisions has been confusion over how much discretion trial judges have to vary sentences beyond the U.S. Sentencing Guidelines, adopted in the 1980s to bring uniformity to prison time and counteract race, wealth and other biases. Judges found that the guidelines sometimes prevented them from dealing fairly with individual circumstances.

The Supreme Court ruled in 2005 that the guidelines should be considered advisory, not mandatory. Now the question is how appeals courts should determine whether a sentence outside the guidelines was "reasonable."

Brian Gall was convicted in Iowa of conspiracy to sell the drug Ecstasy. He was given probation rather than the guidelines' range of 30-37 months behind bars. The judge noted that Gall walked away from the conspiracy at age 21, finished college and started a business. He turned himself in when he was later indicted.

Derrick Kimbrough was convicted in Virginia of selling crack and powder cocaine and sentenced to 15 years in prison rather than 19-22 years under the guidelines. The judge cited Kimbrough's military service, along with the controversy over the disparity in punishments for crack and powder cocaine crimes.

Sentences for dealing crack cocaine are far harsher than those for powder: 1 gram of crack cocaine triggers the same sentence as 100 grams of powder. The Sentencing Commission, which recommended that Congress narrow the 100:1 ratio, says the stiff crack sentence falls disproportionately on black offenders and low-level dealers.

In the Gall and Kimbrough disputes, appeals courts said the judges lacked the latitude to give the lower sentences. The defendants appealed.

Justice Samuel Alito, who spent 15 years as an appellate judge before being appointed to the high court, was an active questioner Tuesday. He challenged Gall's lawyer, Jeffrey Green, on the notion that a judge could show leniency based on a defendant's youth, calling that "a policy question."

To Kimbrough's lawyer, Michael Nachmanoff, Alito suggested judicial latitude on cocaine sentences could pose a dilemma for appellate judges. "What if (an appeals court) sees a number of absolutely identical cases?" he asked. If one sentencing judge used a 1:1 ratio, the next one used 20:1 and the next 50:1, "what is it to do under 'reasonableness' review?" Nachmanoff said that if the judges in those cases had sufficient reasons, the sentences should be upheld.

Justice Department lawyer Michael Dreeben, seeking to win longer sentences for the two men, urged an approach used by many appeals courts. It demands that a sentence varying significantly from the guidelines be justified by a rationale that is equally weighty.

Justice John Paul Stevens wondered if that test was too vague: "How do you measure the strength of the justifications?" Dreeben noted that the differing cocaine penalties stemmed from Congress' view in its 1986 law that crack-dealing spawned more violence. "For a judge to say Congress is crazy," Dreeben said, "is a sort of textbook example of an unreasonable sentencing factor."