Psychopath? Or addicted to his new celebrity?

Is the Washington sniper a psychopath? Or a rational man of cold precision? Does he crave attention for its own sake? Does he want money? Or does he have a more sinister political agenda?

As the hunt for America's most wanted killer continues, teams of psychological profilers are trying to get into the head of the gunman who has killed nine people in suburban Maryland and Virginia. They are not only trying to understand him, they are also busily working out how to communicate with him so he will either make a mistake and get caught, or at least will be dissuaded from killing again.

Informed speculation suggests he has some military training, has reasons to hate the police and is getting a thrill from the terror he is causing.

It became clear yesterday that just about every public comment from Charles Moose, the embattled sheriff of Montgomery County, Maryland, has been scripted by a team of profilers from the FBI.

When Chief Moose lost his temper because a tarot card left at one of the crime scenes was widely discussed in the media, he was not really having a go at the press; he was trying to gain the confidence of the killer, who had left instructions not to publicise the message he had left on the card.

Likewise, when a new message threatening schoolchildren was picked up a couple of days ago, Chief Moose chose at first not to mention it in his regular news briefing. He later released just one line from the message – "your children are not safe anywhere at any time" – but refused to elaborate for fear of inciting more violence.

"It's a coordinated response," one law enforcement official told The Washington Post. "There's a huge desire not to do things that will provoke the shooter."

The FBI is said to believe the killer craves attention, and enjoys seeing the police begging him to get in touch. Chief Moose appealed directly to him through the media over the weekend, asking him to call.

Another assumption seems to be that the stakes are getting higher: the sniper is probably now looking for ways to heighten the thrill – either through greater exposure in the media, or greater taunting of the police, or chasing ever more emotive targets, such as schoolchildren. "The sniper has initiated this, and it is all part of the evolution of this type of offender," said Eric Hickey, a serial killer expert from California State University in Fresno. "The killer has gotten bored. There is only so much control you can exert before the sniper says that he needs more stimulation, he needs another high."

Sniper serial killers are notoriously difficult to catch. Often the shootings are entirely random, making them maddeningly hard to predict. About 40 per cent of cases over the past 25 years are unsolved.

Sniper killers have been known to taunt police for years. In one case in Ohio, where a string of shootings took place between 1989 and 1992, one letter from the killer read: "Don't feel bad about not solving this case. With no motive, no weapon, and no witnesses, you could not possibly solve this crime." The perpetrator, Thomas Lee Dillon, was eventually caught through a tip-off.

No previous case has had quite the media coverage that this one has, and that might in itself account for some of the killer's thinking. "Almost every serial killer who has communicated with police has used a firearm or bomb," said Jack Levin of Northeastern University in Boston.

"That tells me the main motivation is not the killing. It is what happens afterward – holding communities hostage to terror, playing the cat-and-mouse game with police and becoming a big-shot celebrity."