Every Tuesday morning when Ed Rendell was mayor, he traveled from his office on City Hall's second floor up two flights to another man's domain - the office of City Council President John F. Street.

The two, often joined by Rendell's chief of staff, David L. Cohen, talked about sports and family, the week's pressing issues and long-term goals. Rendell took to calling them the "tri-mayors."

The story seems almost quaint now, considering the vitriol that shoots between those floors, and between Mayor Nutter and Council President Darrell L. Clarke. But cooperation between the two branches could make a comeback under the leadership of Mayor-elect Jim Kenney and Clarke, both of whom have spoken well of the Rendell/Street model.

Time will show how those intentions survive the stresses sure to come. But the day after his Tuesday victory, Kenney set the bar high.

"I know my relationship with Council is excellent, my relationship with Council President Clarke is excellent, my relationship with my colleagues that I formerly served with is excellent," he said. "I recognize they are individually elected officials who care about the city, who want the city to move forward. And they have ideas and they have value, and we need to put that all together."

The bridge to Council is arguably one of the most important Kenney can build, with the potential to shape how effectively he can move legislation and, in turn, the overall impact of his administration. He will need Council buy-in on matters ranging from run-of-the-mill legislative efforts to passing a budget to funding the schools.

He has an easy act to follow. Nutter's relationship with Clarke was rocky from the start, largely because of both men's relationship with Street, who was Clarke's mentor and Nutter's enemy.

The relationship grew more contentious with time, notably when Clarke stood by as Nutter was jeered off the Council floor by union members during his 2013 budget address, and when Council killed the mayor's plan to sell the Philadelphia Gas Works without even a holding a hearing.

Kenney and Clarke are clearly starting on better footing, having been colleagues on Council for 15 years before Kenney - after Clarke chose not to run - resigned to run for mayor. Clarke endorsed Kenney in the primary. Both have the backing of John Dougherty, the powerful head of the electricians' union. At least publicly, they have had no major feuds.

Rendell said he felt more hopeful than at any other time since he left the mayor's office that the kind of productive relationship he had with Street could be replicated. He noted that Clarke was a young aide in Street's Council office and present for many of those Tuesday morning meetings. Kenney, he said, seems willing to view Clarke as an equal, which will go a long way.

"It was very important for John to feel like a partner, not a subsidiary," Rendell said of Street. "And I think that's an important thing that Jimmy will have to establish. And if he's always thoughtful and conscious of treating the Council president as a coequal partner, I think he'll do well."

Others are not so sure.

Bill Green, who served with both men on Council and now is on the School Reform Commission, said having Kenney as mayor could shift power on Council, which is already poised for a mild shake-up come January, when four, and perhaps five, new members will join.

Clarke has held huge sway in the fourth-floor chamber, thanks largely to Nutter's strained relationship with members. Kenney does not have that problem.

"Mayor-elect Kenney has the ability to go directly to Council and around the Council president," Green said. "I think they will, for as long as possible, project an outward image of a unified team. And for the city's sake, I hope it lasts. But inevitably there's going to be conflict, and that's when it will get interesting."

Clarke, chronically hard to read and seemingly allergic to speculation, has held true to form when asked to picture how he will work with Kenney.

Is he hopeful for a more productive partnership?

"It will be a different working relationship," the Council president said in a recent interview. "Because it will be a different mayor."

How so?

"It just is going to be different."

How does he want it to be different?

"It doesn't matter," Clarke said. "I'm just saying there's going to be a different mayor. I've been here a couple of mayors now. So as a councilperson, you deal with the person that's in the executive branch. And everybody has their own personalities."

He added that Kenney was someone he respected, someone with roots similar to his own.

"I've known Jim for 20 years," he said. "He grew up in South Philly. I grew up in North Philly, rowhome communities. I know what his priorities are."

Those close to Clarke are more candid. Minutes after the Associated Press declared Kenney the winner, Clarke's spokeswoman, Jane Roh, tweeted a picture of the two side by side, on a tour of Clarke's North Philadelphia district.

"These guys, rowing in the same direction on [education], poverty, criminal justice & quality neighborhoods," Roh wrote. "Can't. Wait."

215-854-2730@TriciaNadolny

Inquirer staff writer Julia Terruso contributed to this article.