Palo Alto residents seeking to enact bans on two-story homes in their Eichler neighborhoods may soon get a little financial aid from the city.

The City Council on Monday sympathized with a growing chorus of Eichler homeowners clamoring for "single-story overlays" in their neighborhoods and agreed to reconsider the fee that the city charges for the zoning change. Under the current system, which aims to achieve cost recovery, residents wishing to apply for a single-story overlay must cough up around $8,000 for the zone change, which also requires support from 70 percent of the neighborhood.

Homeowners in several Eichler enclaves say getting the support of their neighbors isn't the problem. It's the fee that hinders their efforts to protect their generally squat and glassy one-story buildings from taller newcomers. Because Eichler homes typically have glass doors, homeowners worry that their privacy would be violated by multi-story buildings.

In letters to the council and in testimony on Monday night, Eichler homeowners beseeched the council to waive or reduce the fee.

Frank Ingle, who lives in an Eichler home on Richardson Court in Midtown, recently challenged a neighbor who had bought an adjacent property and who proposed to build a two-story home there. After preparing for an appeal, the neighbors ultimately reached a compromise. Yet Ingle noted that the new house is more than twice the size of his own.

"We see a land rush happening in our neighborhood and many neighborhoods," Ingle said. "We'd like to have a collective ability to control this to some extent."

Ingle asked the council to consider waiving the fees for at least a year. Doing so would help the city, he said, because Eichler neighborhoods would have clear rules about what's allowed, and the council would not have to struggle with a parade of appeals filed by Eichler homeowners against their neighbors.

Ben Lerner, a resident of Palo Verde, made a similar request. He noted that the current fee of $8,000 can be raised further, if more work is required for the overlay change. Given the uncertainty, the system in place today is "not very resident or neighborhood friendly."

"I feel that this is not just a partisan issue for a particular neighborhood or a particular homeowner but there's a value to the entire city to preserve Eichlers. ... They are a valued part of Palo Alto's housing tradition," Lerner said.

The city currently has at least eight overlays, including in Greenmeadow, Walnut Grove, Adobe Meadow, Triple El and sections of Midtown and Duveneck/St. Francis.

Councilman Pat Burt said interest in single-story overlay districts tends to correspond to periods of growth, when the number of remodeling and rebuilding projects increase. They come in waves, he said, and the city appears to be in the midst of a wave now.

"We can go from none to a small avalanche," Burt said.

The council didn't rescind the fee on Monday, but council members proved open to revisiting the subject and possibly lowering the fee.

Councilman Tom DuBois led the push to reduce the fee. The city's attempt to recover its costs has pushed up the fee in recent years, he said, and citizens are now being asked to "jump through a bunch of hoops."

The council's Finance Committee discussed the topic during its May review of the fiscal year 2016 budget. The committee voted not to make any changes in the fees at this time, but to obtain more information and deliberate further in the coming weeks before reaching a decision. DuBois favored faster action and urged his colleagues to cap the fee.

"There are policy issues that we should think about, but I think we're also in a heated real estate market," DuBois said. "We can't afford to take a year. People are asking for this now."

DuBois initially proposed setting the fee at $2,000, but later withdrew that proposal in favor of the more open-ended approach favored by Councilman Greg Scharff, who serves on the Finance Committee.

Scharff said the Finance Committee wanted to understand the history of the fee and evaluate different options before making a decision. The goal, he said, was to make the change "at a deliberative and thoughtful manner, rather than just waiving it by not including it in the budget."

Councilman Marc Berman also said he'd like to get more information before making any decisions on the fee.

Councilwoman Liz Kniss agreed. While she observed the growing "sense of urgency" in the community, she supported having the Finance Committee revisit the topic within a month.

Mayor Karen Holman pointed to the surging development climate and the high number of speakers as reasons to act with urgency. The one question that the council already has an answer to is whether there is interest in single-story overlays. The city, she said, has "literally hundreds of homeowners who want protection for their neighborhoods."

Holman agreed with DuBois that the city's individual-review process for approving new homes is "not working." She also noted that the city's Comprehensive Plan talks frequently about the importance of recognizing individual neighborhood and individual characteristics.

"I think it's incumbent for the Council to support that and support the members of the community who support that," Holman said.

After a long discussion, the council voted 6-0, with Councilman Eric Filseth absent, to delve deeper into the subject on June 29.

Vice Mayor Greg Schmid and Councilman Cory Wolbach both recused themselves from the discussion because they live in neighborhoods that could be affected by the fee modification.