Taken together, the decisions reflected the remarkable trajectory the court has traveled in the seven years since it overturned a New Jersey hate-crime statute on the ground that the law gave judges an unconstitutional degree of authority to make the crucial factual determinations that added a hate-crime “enhancement” to an ordinary criminal sentence.

Along with their diminished function under the Sentencing Reform Act of 1984, which set up the federal sentencing guidelines system, federal judges appeared to have been all but ejected from their role at the heart of criminal sentencing.

Judges still may not impose sentences above the range written into law by Congress or state legislatures. But the decision on Monday gives judges broad discretion to impose sentences higher or lower than the guidelines, which are not statutes and are issued by the United States Sentencing Commission.

The two decisions answered questions left hanging in 2005, when the court ruled in United States v. Booker that the federal sentencing guidelines could be constitutional only if “advisory” rather than mandatory. Appeals courts were to review sentences for “reasonableness,” the court said then. But the court did not say what it meant by either “advisory” or “reasonableness.”

Last June, in Rita v. United States, the court ruled that appeals courts could choose to presume that sentences within the guidelines range were reasonable, but that such a presumption was not binding. But that opinion was quite opaque and said relatively little about the trial judge’s role.