Their relationship matters because she is on the public payroll at a salary of $140,000 a year and because of the impact she's had on his mayoralty and the affairs of the city. She controls who gets to see the mayor and when. She is the aide who has his ear after meetings. And according to insiders, she is the person who reinforces his worst instincts, never urging him or pushing him to avoid a fight or to take the high road.

It is telling that even before the Diallo shooting, in the face of the social and economic miracle the mayor is so fond of proclaiming he has engineered, his job approval numbers were not better. Though they peaked at over 70 percent early in 1998, by last summer they'd fallen to 55 percent. And despite his accomplishments, his personal approval ratings have never matched his job-performance numbers.

Would this be different with someone else sculpting his image? Would he have gotten more credit for the drop in crime if there'd been a better communications strategy? Would he have been able to avoid always looking like the bad guy in every fight -- even when he's right -- if someone else had been running his press operation? Would he have reached out more often or built more constructively on his early success with better advice?

It's hard to say. But history shows that whoever has tried to convince the mayor he'd be better off without her -- including lifelong friend Peter Powers -- has ultimately been pushed away. By outworking her enemies and attaching herself to the mayor's side so that there's never an opportunity to badmouth her, she has vanquished her opponents.

"This has increased her influence enormously," says someone who knows her well, "because she no longer has to defend herself and fight those daily battles. None of the people who have joined the administration more recently would even think of taking her on." It's been left to those who've known the mayor longer.

The lack of a coherent communications strategy has frequently turned even victory into a P.R. problem. For example, something as innocuous and as positive as naming a highway for Joe DiMaggio became simply one more ugly political episode -- after the mayor had already gotten his way.

Giuliani wanted to name the West Side Highway after the Yankee legend, while the governor, though uncommitted, had mentioned the Major Deegan. When DiMaggio died, Giuliani and Pataki spoke on the phone, and Pataki, informed that the ballplayer's family preferred the West Side Highway, told the mayor it was okay with him.

"The governor told the mayor," according to someone on Pataki's staff, "that he would talk to the legislature and move the bill forward. So the mayor had won without a drop of blood being shed."

But the next day, the mayor's office released a letter from DiMaggio's lawyer that said a number of unflattering things about the governor. "Clearly, releasing that letter was simply an attempt to embarrass the governor," says the Pataki staff member. "Giuliani had already won."

And so, even though the mayor was going to get what he wanted, he also got a week's worth of bad press about his petty, ego-driven war with the governor. The skirmish had Lategano's fingerprints all over it. "Cristyne told the mayor," according to someone familiar with the circumstances, "that he should release the letter. So the mayor got what he wanted, but thanks to her, not without some damage."

There was even speculation -- denied by DiMaggio's lawyer -- that the mayor's people (read: Lategano) had gotten the lawyer to write the letter in the first place.

The problem Giuliani has now is how to juggle his career plans (he's New York's first term-limited mayor) while facing issues (the Louima trial and the Diallo aftermath) that have the potential to divide the city. Any further missteps could have an impact on his political future.