Edward Dorsey pleaded guilty in June 2010 to possessing 5.5 grams of crack cocaine in 2008 with the intent to distribute it. Under the law in effect at the time of his offense and his plea, and thanks to an earlier conviction, he was subject to a mandatory minimum sentence of 10 years. Under the new law, the mandatory sentence would not have come into play for fewer than 28 grams, and Mr. Dorsey would probably have received a sentence of three or four years.

Judge Evans, writing for a unanimous three-judge panel of the United States Court of Appeals for the Seventh Circuit, in Chicago, said Mr. Dorsey had “lost on a temporal roll of the cosmic dice” and was “sentenced under a structure which has now been recognized as unfair.” But Judge Evans added that the courts were powerless to change things. A solution, he said, was up to Congress.

The Justice Department initially supported that view but later changed its position. The full Seventh Circuit in August declined to revisit the issue by a 5-to-5 vote.

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“Thoughtful people might wonder what sense it makes for Congress, having decided that a 100-to-1 ratio is excessive, to leave the minimum and maximum sentences alone for persons whose crimes predate Aug. 3, 2010,” Chief Judge Frank H. Easterbrook wrote in explaining why the full court declined to rehear four appeals presenting the issue. “It is a good question, to which there is no satisfactory answer other than the observation that legislation is an exercise in compromise.”

A dissenting member of the full court, Judge Ann Claire Williams, asked a different question. “Why would Congress want sentencing judges to continue to impose sentences that it had already declared to be unfair?” she asked, adding, “There is no good answer to this question.”

In a second dissent, Judge Richard A. Posner, said that requiring sentencing under the old law after the new one came into force was “perverse” and “gratuitously silly.”

The case involving Mr. Dorsey is Dorsey v. United States, No. 11-5683. The Supreme Court also agreed to hear a companion case, Hill v. United States, No. 11-5721, and it consolidated the two for argument.

The second case involves Corey Hill, who was convicted in 2009 of selling 53 grams of crack cocaine in 2007. He was sentenced under the old law in December 2010, after the new one had come into force.

In the lower courts, the Justice Department successfully urged the imposition of the harsher sentence called for by the old law. In the Supreme Court, it reversed course, urging the justices to hear Mr. Hill’s appeal and to rule in his favor.