Cash for police work is dwindling at City Hall and in Washington. Civilian members of the force are facing layoffs. Station houses are not ideally staffed. More than 1,000 officers remain assigned to counterterrorism duties. At 1 Police Plaza, every transfer and promotion now requires the approval of Commissioner Raymond W. Kelly. At the Police Academy, the flow of new recruits has slowed to a trickle.

Yet despite these challenges, crime is down in New York  more significantly than in several other big cities around the nation. Murders, which hit 200 at the midyear point, are heading toward a new low. (The peak was more than 2,200 in 1990.)

That accomplishment has impressed many observers.

“The stress that his department is under right now is enormous,” Peter Vallone Jr., the chairman of the City Council’s public safety committee, said of Mr. Kelly. Mr. Vallone said it was, then, remarkable that the police had been able to maintain, and even improve upon, critical aspects of crime fighting in recent years.

Given the reduction in the force’s size, and the intensity of its efforts to combat everything from global threats to outbreaks of car thefts, the Police Department might well be at something of a crossroads. So far, though, there have been no obvious outward signs of problems.

That said, not even the department’s most senior officials deny that they have had to adjust and improvise as they have faced shrinking numbers of officers and civilian personnel. One measure of that has been the department’s increased reliance on a tactic known as predictive policing, trying to use crime statistics and other information to forecast where crime may pop up next.