For those who embrace the notion of personal responsibility, such a change in public attitudes might be considered progress. But in Mexico, what suggests an increase in tolerance of illegal drug use in the U.S. has a tragic flipside: the gut-wrenching violence that arises when demand meets prohibition. This country is paying dearly for that contradiction.

Under prohibition, only criminals can serve the market for illegal narcotics. And they have a lot of incentive to do so since prohibition pushes prices up. These market dynamics have given rise to transnational crime networks -- modern, savvy businesses run by ruthless killers bent on preserving their income. Anyone who tries to get in the way risks becoming a statistic. Last year in Mexico there were 2,713 homicides attributable to organized crime, up from 2,120 in 2006 -- according to the intelligence arm of the country's attorney general.

It's a pretty grim picture. Yet there is at least one man in Mexico who believes that it doesn't have to be this way. His name is Eduardo Medina Mora, and 14 months ago he chose to accept what some would regard as mission impossible: taking on the job of attorney general with the express goal of restoring order to a nation turned upside down by organized crime.

I interviewed him last year, just 100 days into his new job, and I met with him again two weeks ago to take a reading on progress. He reports that the Mexican state is reasserting itself, though he also warns that the battle is far from won.

Mr. Medina Mora suffers no illusions about his office's capacity to shut off the supply of drugs to the U.S., or for that matter in Mexico, where drug use is on the increase. That's a welcome relief: After decades of a war on drugs claiming thousands of innocent lives, poisoning institutions in developing countries, and raising the incentive for pushing narcotics on children -- all the while delivering not a modicum of success -- the argument for attacking supply to end demand is by now tedious.

Instead, Mr. Medina Mora is a realist. "The objective," he says, "cannot be destroying narcotrafficking or drug-related crime, because demand is inelastic." "It is very important not to lose perspective on the goal," he tells me. "Trying to get rid of consumption and trafficking is impossible, as a bold objective."

This in no way implies surrender on his part. What's important, he says, is that the goal be clearly understood. Instead of focusing on supply, he is concentrating on the suppliers, and specifically their ability to run business empires. It's about removing "the enormous economic and fire power" of the cartels which threaten the Mexican democracy, and "recovering the territory [controlled by organized crime] for the people and the state." This view is not unlike that of Colombia's President Álvaro Uribe, who has led the fight to end the tyranny of organized crime in some parts of his country.

In Mexico, Mr. Medina Mora continues, "there are areas where organized crime disputes the state's exclusive use of force and its power to collect taxes. They are not only shipping drugs but they are involved in extortion, prostitution rings, smuggling goods and people, stealing Pemex [the state-owned oil company] products, and forcing legal businesses to pay protection taxes."

The attorney general's strategy has been to hit these businesses where it hurts most: in their pocketbooks. By studying the way the narcotics market works, his office has used "operational mapping and mapping of their supply and distribution routes" to "put obstacles in the way and block traditional flows." This approach involves tighter controls on air traffic, better technology and smarter inspection systems for shipments from South America.

Mr. Medina Mora says the plan is working, and rattles off a string of captures and seizures, including some 10 drug-trafficking planes -- even one DC-9 -- large enough to carry up to five metric tons of cocaine. Last year he reeled in a 23.5 metric-ton shipment of cocaine coming by sea from the Colombian port of Buenaventura, and broke up a Mexico City operation that allegedly supplied "meth" producers annually with over 100 metric tons of the precursor pseudoephedrine.

The attorney general is rightly proud of this record, and says that lower availability has meant sharp increases in the street price of both cocaine and "meth" in 38 cities in the U.S. -- according to U.S. officials. Still, the seizure scorecard does nothing to prove progress in the battle against drug use, any more than body counts reveal who is winning a war. And as prices rise so do cartel incentives, particularly when demand is notoriously resistant to change.

But going by Mr. Medina Mora's measure of success -- which is damage to organized crime such that it ceases to dominate Mexican territory and society -- there may be progress. Unfortunately, he says, proof of that could come in the form of more violence in the short run. "When this kind of criminal network begins to collapse, the criminals go back to more primitive methods of crime -- kidnapping, car theft and extortion. They fragment and lose control; cells start operating on their own and fighting with each other. Turf becomes very important."

As if to prove his point, two days after we talked a bomb exploded in the trendy neighborhood of Zona Rosa here. A government investigation is ongoing, but there is reason to believe that the device was meant as payback to law enforcement for the arrest two days earlier of seven members of the powerful Sinaloa cartel.

Mr. Medina Mora believes more could be done with greater international cooperation against money laundering, and with a U.S. effort to stem the flow of high-powered weapons into Mexico. Another way, which he is too polite to mention, would be for U.S. authorities to acknowledge that under present policies they are losing their drug war.

Write to O'Grady@wsj.com