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Mayor Rahm Emanuel and police chief Garry McCarthy are sticking to their script on police staffing: we're all good.

After Governor Pat Quinn announced this week that he was sending 40 state troopers to help Chicago police round up fugitives, city officials labored to let the public know that they welcomed the help even though they don't really need it.

Mayor Rahm Emanuel stressed that the state troopers would simply join Chicago police who are already serving warrants and apprehending fugitives in high-crime neighborhoods. Police superintendent Garry McCarthy echoed his boss's comments.

"Our fugitive team [was] expanded a couple of years ago," the police chief told the Sun-Times. "We think we have it right-sized. But more means we can go out and arrest more wanted people, which is obviously going to help us."

In other words, the city of Chicago has all the police it needs—except that if it had more, it could get more lawbreakers off the street and potentially make the city safer.

This is what's called doublespeak.

As a mayoral candidate, Emanuel promised to add as many as 1,000 police officers to the ranks. Once he had the job and was in charge of the budget, he switched to saying that he was moving more cops to the street. Then, after shuffling hundreds of officers around, he announced that he'd successfully added more than 1,000 "to the beat."

What Emanuel hasn't mentioned is that the number of police officers on Chicago's force has dropped since he's been mayor. In June 2011, shortly after he was sworn in, there were about 10,900 officers on the city payroll, records show. Now there are about 10,600.

That's potentially 100 fewer cops working around the city at any given time.

For three years, the mayor and police chief have been pointing to carefully packaged statistics and proclaiming that crime is lower than at any point since the mid-1960s.

"Our strategy is working," McCarthy told reporters Thursday.

Yet as the police chief acknowledged, Chicago is still rocked by outbursts of violence, and a key part of his strategy is sending more cops to the city's high-crime hot spots. But the mayor has decided it's too expensive to pay for additional salaries and benefits. So instead of adding full-time officers—or even keeping pace with retirements and attrition—McCarthy has implemented a "violence reduction initiative" that pays police overtime to work additional shifts.

Last year the overtime pay added up to more than $100 million. That's apparently considered a bargain compared with the cost of maintaining the ranks.

Cops like the overtime money—who wouldn't? But isn't it possible that working double-time at one of the most dangerous and stressful jobs in the world could take a toll?

Being Emanuel's man, McCarthy won't concede it. "I was an overtime guy," he told me last year. "I did a ton of overtime, and I'm still doing it."

Mayors and police chiefs prefer to stick to the narrative that they've got things under control.

During a spike in violence in 2008, then-governor Rod Blagojevich had the audacity to declare that the bloodshed in Chicago was in fact "out of control." His offer of state police patrols and National Guard helicopters incensed Mayor Richard Daley, who shot back that the governor had cut funding for law enforcement programs. "What help can he give me?" Daley said.

Out of the spotlight, they agreed that state troopers would increase patrols around high-crime neighborhoods and help with gun investigations.

Violence was still battering some of the same neighborhoods two years later, when state reps John Fritchey and La Shawn Ford called on Daley to seek assistance from the National Guard, either for additional patrols or administrative support. Daley rebuffed the two legislators, saying that if they really wanted to help they'd go back to Springfield and pass stronger gun laws.

Fritchey, who's now a Cook County commissioner, says he's happy to hear that Emanuel is accepting backup from Governor Quinn. "Obviously, anything that helps get bad guys off the street is a good thing. But nobody should accept this as a solution, short term or long term, to the issue that we don't have enough police officers on the street on any given day."

"If Superintendent McCarthy's police tactics are working, that's fantastic," Fritchey adds. "But I find it hard to believe that even he wouldn't like more manpower."

The optics are crucial.

On Thursday McCarthy appeared with U.S. attorney Zachary Fardon, state's attorney Anita Alvarez, and federal agents to announce the most recent takedown of a west-side drug operation. The authorities said the business, led by high-ranking members of the Gangster Disciples, had been dealing heroin and cocaine for more than 20 years and protected its profits with guns.

McCarthy praised the teamwork between police and federal and state investigators. But when asked about the assistance coming from the state, McCarthy again downplayed it. "The state police will be supplementing our fugitive enforcement," he said.

Ours.