Call it the case of the disappearing police officers. While the number of Los Angeles Police Department officers has grown over these past few years, the city's residents are today seeing fewer of them on the streets. And in the new year they'll see even fewer. It's the kind of mystery that will make you want to call the cops.

Los Angeles has long been known as one of the most under-policed cities in the country. According to the FBI's Uniform Crime Report for 2009, the LAPD had 2.59 officers per 1,000 in population last year. That number may seem meaningless until one puts it alongside the figures for two comparable cities: New York had 4.17 officers per 1,000 residents, and Chicago had 4.59. In 2006, the Los Angeles city council approved an increase in residential trash fees, the revenue from which was to be devoted to expanding the police department.

And while the LAPD has indeed expanded, with the number of officers increasing from just under 9,400 in 2006 to almost 10,000 today, on any given day there are fewer of them working the streets. And soon, owing to a set of circumstances only a government bureaucrat can understand, there will be even fewer.

So what's going on? Los Angeles, like most American cities, is coping with the effects of the sluggish economy, with tax revenues on the decline even as demand for public services continues to grow. Mayor Antonio Villaraigosa puts the current city deficit at $485 million, and one of the methods he has chosen to cope with it is a freeze on most hiring in the municipal workforce. The LAPD has been exempted from the freeze except as it relates to civilian employees such as record clerks and jailers, on whom the department's police officers depend to keep the machinery running.

But as the department's civilian workforce shrinks, police officers are being removed from field duties and called on to do tasks ordinarily performed by these now-absent civilians. Early next year, for example, nearly 100 sworn officers will be working the LAPD's Metropolitan Detention Center, a new jail that will take the place of the one in Parker Center, the decrepit and all but vacated former headquarters building. For reasons known only to them and God, the people entrusted to make such decisions have determined it is somehow more cost-efficient to supplement the jail's staff with police officers than to hire and train a sufficient number of jailers.

Making matters worse is the LAPD's attempt to limit overtime worked by police officers. Every cop knows that any arrest made within three hours of his scheduled end-of-watch is going to result in overtime, and if he works any shift other than day watch, it's going to be followed by at least one court appearance for which he will also be owed overtime. In years past the city attempted to compensate as much overtime as it could in cash rather than time off, thus leaving as many cops as possible on the streets. Today, cash overtime is all but a memory, so as officers accumulate overtime in excess of 250 hours, they are ordered to take as much time off as required to bring their balance below that level. The result is that on any given day, hundreds of officers are on unscheduled days off. And when you consider that in a typical month, fewer than 3,000 of the nearly 10,000 officers on the LAPD roster are deployed in patrol assignments, you are left with a pretty meager force for a city of 4 million people spread over 469 square miles.

At least so far, LAPD Chief Charlie Beck has been able to operate under these budget constraints without seeing the rise in crime one might have expected. Part I (i.e., serious) crime in the city is down more than seven percent from last year, and every one of the LAPD's 21 patrol stations has seen at least a modest decrease. Given these figures, Mayor Villaraigosa and the city council may assume they can afford to skimp on the LAPD's budget without paying too high a political price.

But the Los Angeles Police Protective League, the labor union that represents rank-and-file officers (and of which I am a member), has proposed that the city refrain from hiring new officers, and that the resulting savings be devoted to resuming the payment of cash overtime. This, the League maintains, would have the effect of immediately returning to the field those hundreds of officers who would otherwise remain idled due to forced days off. In an op-ed piece published in the Los Angeles Times on Dec. 2, League President Paul Weber makes the case that the taxpayers of Los Angeles have been swindled, taken in by a bait-and-switch scheme that promised more cops on the streets but failed to deliver. Yes, the officers were hired, but what good are more police officers if so many of them are diverted into clerical and other non-patrol duties or are forced to stay home because they've racked up too much overtime?

For their part, Chief Beck and Mayor Villaraigosa counter that a complete freeze on hiring police officers would have serious consequences for the LAPD in the future. Experience has shown that when the apparatus of recruiting, hiring, and training new police officers is shut down for any appreciable period, it becomes a formidable task to get it up and running again when economic conditions improve.

And there may be a reckoning ahead. Overall crime may be down in Los Angeles, but seven of the city's patrol areas have seen increases in homicides this year, and 12 have seen increases in the number of shooting victims. City-wide, the number of shooting victims is up more than five percent over last year. These are the crimes that frighten residents most and motivate them to pick up the phone and hector their local police captain or city councilman with questions about what they intend to do about all this bloodshed.

But there may not be much they can do if an underfunded LAPD is faced with the sort of crime figures that were common a few years ago. In 2001, for example, there were 484 Part I crimes in Los Angeles for every 10,000 in population. That number has fallen steadily since, and in 2009 the figure was just 242, exactly half of what it was only eight years before.

That dramatic drop in crime was brought about through a concerted effort on the part of city leaders to fund and maintain a police department capable of confronting what in many parts of Los Angeles was an unchecked criminal subculture, the members of which reveled in terrorizing their law-abiding neighbors. That criminal subculture still exists today, though it's impact has been largely diminished through the efforts of the men and women of the LAPD.

The fight against crime is like a tug-of-war, where even a slight shift in momentum can turn winners into losers. For ten years now the momentum has been on the LAPD's side, but the city's bleak financial picture may change that. You won't want to live or visit here if it does.