The Audubon Commission will make a few more tweaks to a proposal aimed at ensuring it gets adequate public input on projects that would infringe on green space in Audubon Park or other Audubon facilities.

After critics at a public hearing argued the first proposal would still allow too many projects to slip through the cracks, the commission voted unanimously Thursday to delay action on the resolution while it works out ways to include smaller projects and to increase the time for the public to comment on projects that would replace open space at any of the commission’s parks.

The proposed self-imposed requirements, and the willingness to make them even more comprehensive, come as a reaction to widespread opposition to the proposed construction of a $4 million soccer complex at “The Fly,” the riverfront section of Audubon Park.

Opponents, who succeeded in getting that project scrapped last month, argued that the proposed facility had flown below the public’s radar until just before ground was due to be broken, preventing those who wanted the site to remain open space from raising their concerns until almost the last minute.

The clash over the soccer complex has left many skeptical of the commission’s overall strategy for the parks under its control, and more than a dozen speakers at Thursday’s meeting called for greater transparency.

The proposal before the commission would have ensured that to some extent, but its critics argued it didn’t go far enough.

The plan would have required public outreach — including news releases, notifications to the offices of City Council members and the mayor, and a special public hearing — for any project that would result in the elimination of an acre or more of green space. The hearing would have to be scheduled at least 30 days before a vote on the project could be taken.

But many speakers said those requirements would still allow smaller projects to encroach on open space in the park in a piecemeal fashion and would not provide enough time for residents to voice their objections.

“I’m here supporting public participation but not what you’ve put forward,” Debra Howell told the commission. “There are many restaurants, sports facilities, that can fit on less than an acre of land. For example, if the commission decided to double the size of the golf (clubhouse) restaurant, it would not require any public notice.”

In the face of that and similar criticisms, the commission agreed to work on the plan further before voting on it.

“I think the discussion, particularly regarding the timeframes and the footprint, is a good one,” Commissioner Bart Farris said.

Commissioners began working on the plan at the urging of City Councilwoman Susan Guidry, whose district includes Audubon Park, in the wake of the controversy over The Fly.

“I think we all learned how important that property is to the citizens through what’s just recently happened,” Guidry said. “And, of course, it shines a spotlight on what the process is that doesn’t work there.”

Guidry encouraged the commission to adopt policies similar to the city’s Neighborhood Participation Program, which is designed to get input from residents on proposed developments as they’re taking shape.

Some speakers said the recent controversy showed that more than just better public outreach is needed and that a revamping of the commission, a city agency, is in order.

“Public comment periods are nice. It’s great that you want to listen to the citizens of New Orleans about how we’d like our public parks to be governed, but I’d like to note that we don’t have a single, democratically elected voice at this park,” Christopher Lane told the commission. “Ask the City Council to consider changing your charter to have an elected commissioner; ask the mayor to appoint members of a community or neighborhood organization nearby to this board.”

Follow Jeff Adelson on Twitter, @jadelson.