WASHINGTON — The amount of opioid painkillers prescribed in the United States peaked in 2010, a new federal analysis has found, with prescriptions for higher, more dangerous doses dropping most sharply — by 41 percent — since then.

But the analysis, by the federal Centers for Disease Control and Prevention, also found that the prescribing rate in 2015 remained three times as high as in 1999, when the nation’s problem with opioid addiction was just getting started. And there is still tremendous regional variation in how many opioids doctors dole out, with far more prescribed per capita in parts of Maine, Nevada and Tennessee, for example, than in most of Iowa, Minnesota and Texas.

Over all, the analysis found that the amount of opioids prescribed fell 18 percent from 2010 to 2015, though it increased in 23 percent of counties.

“We still have too many people getting medicine at too high a level and for too long,” said Dr. Anne Schuchat, the acting director of the C.D.C. She noted that the quantity of opioids prescribed in 2015 would be enough to provide every American with round-the-clock painkillers for three weeks.