WASHINGTON — Federal judges have broad leeway to impose shorter prison terms for crack cocaine and other crimes, the Supreme Court said yesterday in a pair of cases that bolster arguments for reducing differences in sentences between crack and powder cocaine.

The court, by 7–2 votes in both cases, upheld more lenient sentences imposed by judges who rejected federal sentencing guidelines as too harsh.

The decision was announced ahead of a vote scheduled for today by the U.S. Sentencing Commission, which sets the guidelines, that could cut prison time for as many as 19,500 federal inmates convicted of crack crimes.

Justice Ginsburg, writing for the majority in the crack case, said a 15-year sentence given to Derrick Kimbrough was acceptable, even though federal sentencing guidelines called for Kimbrough to receive 19 to 22 years.

“In making that determination, the judge may consider the disparity between the guidelines’ treatment of crack and powder cocaine offenses,” Justice Ginsburg said.

The issue has a strong racial component. Kimbrough, a veteran of the first Gulf War, is black, as are more than 80% of federal defendants sentenced in crack cases. By contrast, just over a quarter of those convicted of powder cocaine crimes last year were black.

The Sentencing Commission recently changed the guidelines to reduce the disparity in prison time for the two crimes. New guidelines took effect November 1 after Congress took no action to overturn the change. Today’s vote is whether to apply the guidelines retroactively.

Yesterday’s Supreme Court ruling grew out of a decision three years ago in which the justices ruled that judges need not strictly follow the sentencing guidelines.