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But the same period saw violence and murder rates soar in Mexico, turning entire regions of the nation into havens of unchecked criminal activity.

Drug production appears to be on the rise.

Marijuana and opium cultivation in rural Mexico has expanded “significantly,” according to an August 2011 report by the Congressional Research Service.

“In 2009, estimated marijuana production in Mexico rose to [43,000 acres], a 45 percent increase over 2008 and the highest level recorded since 1992,” the report said.

Similar statistics hang over Colombia, where the United States spent about $7 billion supporting a drug war during the early 2000s that included widespread aerial crop-eradication campaigns.

In Latin America, Colombia remains the No. 1 cultivator of coca, the essential ingredient in cocaine, according to a 2011 report by the International Narcotics Control Board, an independent monitoring organization tied the United Nations.

Coca production also has increased in neighboring Peru.

“If you’re defining your game as reducing cocaine in Colombia, you’re probably still in the sixth inning, and you may be playing the wrong game,” said Adam Isacson, senior associate for regional security policy at the Washington Office on Latin America.

Mr. Brownfield’s optimism toward Mexico may also be premature, said Michael Shifter, who heads the Inter-American Dialogue in Washington.

“Hopefully we are in the sixth inning and one could point to signs that lead to an optimistic view,” Mr. Shifter said. “But it’s by no means certain or assured.

“The successes we’ve seen haven’t lead to a real overall improvement that’s sustainable,” he said.