The U.S. Federal Reserve agreed to cut interest rates at its December meeting only after a deeply nuanced debate about the risks facing the U.S. economy right now, according to minutes of the latest two-day session.

Even some of those who supported the rate cut acknowledged “the decision was finely balanced or that they could have supported keeping the target range unchanged,” given the different risks facing the U.S. economy, according to the minutes released on Tuesday.

In economic projections released after the December 9-10 meeting, six officials outright opposed a cut and two of that group dissented as........

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