HERE ARE three suggestions.

Make public safety priority number one. Last year, there were 68 homicides in the city — the most in five years. The increase in crime prompted outgoing New York mayor Rudy Giuliani to crow in his farewell address that New York’s "low tolerance" method of fighting crime was superior to Boston’s model of community policing. After Giuliani’s remarks, Menino and Police Commissioner Paul Evans were quick to defend Boston’s record on crime. But that’s what you’d expect them to do.

"One role for the council is to force the mayor and commissioner of police to think through what they’re doing and ask if the police department is doing everything it could be doing," says one observer. "Is the Boston model [of policing] something we want to stay with? The mayor clearly doesn’t want to talk about it."

Indeed. Late last year, Menino downplayed the significance of the city’s rising homicide rate by noting during a mayoral debate with Davis-Mullen that most of the homicides were taking place inside buildings rather than on the streets and that they were related to domestic violence.

"If [the council] had some foresight, they would understand that we have a rising population of young people, which inevitably brings more crime," says Nucci. "I think they should try to get ahead of that curve."

Ross, for one, is ready for the challenge. "We all want to see more police officers on the street," he says. "The 60-plus homicides that took place last year is alarming."

But there aren’t going to be more cops on the street unless the city pays for them. That’ll take some tough decisions, come budget time. And some tough negotiating when the police contract comes up for renewal this year.

Take a leadership role in the public schools. The school committee is appointed by the mayor, which means it "doesn’t represent parents and taxpayers," says one observer. City council should pick up the slack.

Forcing the mayor to make funds available for the purchase of books was a good start. But the council can’t let up. In truth, the money allocated last July was a band-aid measure. "There is continuing concern around making sure students have books and supplies and making sure teachers aren’t being exploited in terms of having to use their own money to buy supplies," says Councilor Chuck Turner of Roxbury.

In the meantime, about 60 percent of Boston district high-school students who took the MCAS test in their junior year flunked. What’s going to happen if the city denies diplomas to a majority of its students? Why isn’t the mayor talking about this? Why isn’t schools superintendent Thomas Payzant making a big deal of this? If they won’t, the city council should.

Stop rubber-stamping the mayor’s budget. The next chair of the council’s Ways and Means Committee has a big job ahead this year. "It’s easy to be slothful when money’s pouring through the door," says an observer. But those days are over — as the mayor himself noted during his inaugural address. The council can play a proactive as opposed to reactive role in the process by dissecting the budget ahead of time and trying to do "some agenda-setting for various departments."

To some extent, Davis-Mullen did this last year, but so much of her effort was tied up with her mayoral campaign agenda that its impact was lost. But this year’s council can build on what she started last year. "Our chief responsibility is to oversee the budget," says Turner. "[Last year] there was a major struggle around education in terms of monies for books and supplies. The council and the GBIO were able, for the first time in years, to produce a plan."

By being more forceful and proactive, the council can essentially push through any agenda it wants. Turner, for one, would like to "build a line item into the budget with money for affordable housing."

To accomplish anything, though, the council will have to get organized and show that it can come up with an agenda and see it though — and work with the mayor. Flaherty’s election as council president all but ensures the latter. But not the former.

Susan Ryan-Vollmar can be reached at svollmar[a]phx.com