When the city went back to the drawing board last year after failing to conclude a deal with its chosen developers for the former World Trade Center building, it made a critical adjustment to the rules governing the selection process for the site.

This time around, instead of picking just one development team with which to negotiate, the city gave itself the right to deal with as many suitors at a time as it wants. The adjustment, intended to force the developers to try to top one another’s offers, may begin to pay off this week.

The five teams in the running to redevelop the vacant and bedraggled but exceptionally well-located 1960s office building at the foot of Canal Street each raised their bids to the city on Tuesday, a week before a selection committee will decide which team or teams the city will negotiate with to turn the 33-story structure into a hotel and residences.

Some of the developers declined to provide details of their revised proposals, but each confirmed offering to pay the city more in rent than it initially proposed last month. Three teams also tweaked other details of their proposals.

Some of the teams also have been putting out news releases touting their proposals and occasionally criticizing some of their rivals’ ideas.

The city moved to amend the selection process rules after failing to come to an agreement on financial terms, including the office tower’s value, with Gatehouse Capital and DAG Development. That team’s proposal to convert the building into a W Hotel and apartments beat out two other proposals in the last round to win the exclusive right to negotiate a 99-year lease agreement for the site with the city.

After announcing last year that the city would solicit a new round of proposals, Deputy Mayor Cedric Grant said reserving the right to negotiate with several bidders was both a matter of following best practices and an effort to guard against a repeat of the prior round’s debacle, by pitting developers directly against each other in the negotiation process.

After giving the developers more than a month to study the other proposals and to check each other out in person at a public meeting Feb. 27, the city called for “best and final” offers last Tuesday.

“Like everyone else, we tried to put our best foot forward, at the invitation of the city,” said local developer Darryl Berger, whose team has proposed a $292 million Conrad Hotel and branded residences at the site. “We took a hard look at what was the best we thought we could do in all circumstances.”

Berger’s team, called 2 Canal Redevelopment LLC and including fellow local developers Joe Jaeger and Roger Ogden plus Xavier University President Norman Francis, added a letter from the Howard Hughes Corp. to its original bid. Hughes, which owns the Outlet Collection at Riverwalk, said it has signed on as a partner in the planning of that team’s project and is considering becoming an investor.

The agreement with the Outlet Collection at Riverwalk owner would seem to strengthen the team’s long-term vision of redeveloping a large stretch of riverfront property, including connecting both the Morial Convention Center and the former WTC building to the Hilton New Orleans Riverside Hotel, connecting the Outlet Collection at Riverwalk to Convention Center Boulevard and making “significant aesthetic and practical enhancement” to Poydras Street.

Mayor Mitch Landrieu has made “turbocharging the riverfront” a central part his campaign to improve the city before its tricentennial celebration in 2018.

Berger said the 2 Canal team also revised its economic proposals in its final pitch, though he declined to provide details. The team originally offered an upfront payment of about $50 million in one option and, in a second option, half that amount upfront, along with $1.5 million annual rent.

HRI Properties, which has proposed a 309-room hotel with 261 residential units operated by the Luxury Collection of Starwood Hotels & Resorts, also would not provide specific details of changes in its proposal. But company President Tom Leonhard said the changes include a larger upfront deposit and increased base rent.

“We did sweeten the deal for the city,” Leonhard said.

HRI previously proposed making a $10 million upfront lease payment to the city and a base rent payment of $1.75 million a year. The city also would have received 41 percent of the net profit from an interactive visitor attraction called the New Orleans Experience at the site.

Leonhard said HRI revised its proposal to offer the city a share of the gross profit, instead. He said HRI did not propose any changes to its original physical designs.

An attorney for Two Canal Street Investors Inc., which scored highest in a first round of evaluations narrowing the projects under consideration from 10 to five, said that team has altered its financial proposal to include more money to the city upfront. Instead of offering a nonrefundable payment of $23 million and annual payments of $5 million during construction and $2.5 million a year when renovations are complete, the developers now are offering $65 million upfront. That amount includes an additional $42 million in prepaid rent for 30 years.

Two Canal Street has proposed a $238 million, 318-room Hotel Alessandra and 240 luxury apartments called the Alessandra Residences.

That team also would give the city $3 million a year in rent from a separate attraction it has proposed building next to the former World Trade Center structure. As part of its updated proposal, Two Canal Street says it would partner with US Thrill Rides to build a 320-foot-tall structure called the Tricentennial Tower. The structure would feature a gondola-type ride that scales the tower in a double-helix formation, plus a restaurant with an observation deck. The team likened the attraction to Seattle’s Space Needle.

Meanwhile, the president of Carpenter & Co., which with its partners has proposed turning the building into a Four Seasons Hotel, said it also has “modified a lot of the economic prospects to increase them.” However, Dick Friedman would not provide specifics of the change.

The team’s original proposal offered $2 million a year in rent for the first five years of operation; $2.25 million annually in years six through 10; and $2.5 million from years 11 through 15. The proposal for a 350-room hotel with 76 residences also called for rent payments after the 15th year to climb to $2.5 million times the percentage increase in the consumer price index for the preceding five years, with some restrictions. The developers also initially proposed giving the city a share in the hotel’s profits and an additional $7.5 million over nine years if it were to receive federal and state historic tax credits for the project.

The team’s revised proposal also eliminates a request to rent the World Trade Center parking garage near the Hilton Riverside Hotel and proposes instead to build a new garage next to the existing building.

“We’re not going to have any gimmicks or anything other than a high-quality project, high-quality design,” Friedman said.

John Rutledge, president of Oxford Capital Group, which has proposed a 516-room Godfrey Hotel plus 166 one- and two-bedroom apartments and six penthouse apartments at the site, said the team increased its base rent and upfront deposit in its revised proposal. Oxford initially offered a base rent of $1.85 million that would increase each year based on the consumer price index. Additionally, it said it would give the city 3 percent of annual revenue over $45 million.

A five-member selection committee will evaluate and rate the revised proposals Tuesday. The panel comprises Chief Administrative Officer Andy Kopplin; Cindy Connick, executive director of the Canal Street Development Corp.; Bill Gilchrist, the city’s director of place-based planning; City Planning Commission Executive Director Bob Rivers; and Ashleigh Gardere, executive director of the city’s Network for Economic Opportunity.

The committee is being advised by Scott Whittaker, an attorney with Stone Pigman, and real estate specialist Greg Hartman, with Jones Lang LaSalle.