A plan to change the terms of leases to land at Lazy Point in Amagansett, where residents own their houses but rent the land beneath from the East Hampton Town Trustees, hit a small roadblock during a public hearing on Monday when some homeowners objected to the proposed extension of their leases from the present one-year term to 35 years. Real estate at Lazy Point is anomalous on the South Fork, home to some of the most expensive property in the country. Rents remain as modest as the small lots on which the mostly unassuming houses sit. When the trustees, who derive about half their annual income from the leases, raised the annual rent by 50 percent in 2013, the new figure was just $1,500. Tenants, who must be residents of the town, pointed out Monday that because they do not own the land, they cannot get a mortgage to help buy a house or make improvements to one. After contentious negotiations in 2015, terms were modified to include an annual 2 percent rent increase and a 2 percent transfer fee, assessed to both buyer and seller when a property changes hands. Over time, the trustees warmed to tenants’ calls to modify the lease terms at the bucolic neighborhood on Gardiner’s Bay in a way that would allow them to obtain mortgages. On Monday, Jim Grimes, a deputy clerk of the trustees who heads the governing body’s Lazy Point committee, referred to the 2015 negotiations as “somewhat of a crisis” in the tenant-trustee relationship, “in terms of how they were going to compensate our community” for the right to live in the unique and idyllic setting.“One of the things that’s come up over the last several years is how the demographic of the community has changed over time,” Mr. Grimes said, “how every time a property comes up for sale it’s immediately gobbled up” — by a resident, yes, but “a resident who has the cash to put down” or an asset that can be leveraged. Not only does that preclude many would-be residents, he said, “but what it’s also done is impacted the present community as a whole. A lot of people down there are in the latter part of their lives, they may want to upgrade their properties, either in advance of trying to turn them over to relatives or just to live there themselves.”Annual leases, Mr. Grimes said, never provided Lazy Point tenants “any form of equity that they can take to a lending institution and secure some kind of financing. . . . This 35-year lease extension which we’re proposing here tonight is to try and mitigate that somewhat, to give the people of the community the opportunity . . . to try and secure financing, but second to that, also to secure the relationship with our tenancy over a longer period of time. There is never, probably, any good reason to go from year to year with these leases,” he said. “It doesn’t create a good dynamic with your tenants if you’re just living on an annual basis.” As stewards of the land, he added, “We recognize that if our tenancy is comfortable and feels safe and secure, we and our revenue stream will manage to be safe and secure. That was the point of this.” His remarks drew applause from the many Lazy Point residents in attendance.David Seeler, president of the Lazy Point Neighborhood Association, told the trustees that long-term leases would provide the security that Mr. Grimes described. Tenants, he said, have long maintained the trustees’ property, installing snow fencing, planting beach grass, and cleaning up not only the beach but also access roads. “It’s a concern of ours to preserve this beautiful asset the trustees have,” he said. “I do want to thank the trustees for the amount of time they’ve put into this.”But there were questions and comments. Reg Cornelia, who lives in Springs but formerly lived on private land at Lazy Point, said that, given their own financial responsibilities, the trustees should seek more for themselves in the landlord-tenant relationship. Those responsibilities include dredging of bottomlands under their jurisdiction and litigation when there are challenges to land they control, which includes most beaches west of Montauk. He suggested a transfer fee of between 6 and 10 percent, which would offer “a substantial amount of income for the trustees,” particularly on a sale exceeding $1 million. Mr. Grimes was reluctant. “That was part of the crisis four years ago,” he said, referring to a now-former trustee who had proposed changing the lease from $1,500 per year to $1,500 per month. “These people pay taxes. How do you reconcile that 6 percent . . . to a possible buyer that’s a working guy that’s going to secure financing? One of the unique and positive things is the fact that we’ve worked really hard to have a good relationship with our tenants. One thing that sours feelings is a feeling that everybody has to maximize their property.”Mr. Grimes may have spoken for many lifelong residents of East Hampton. “We lament how expensive all our real estate has become. But the hard fact is, that’s being promoted on a regular basis, and is pushing some of the other people aside.” Elaine Jones of Amagansett told the trustees that a banker with Chase Private Client said the institution would not offer a mortgage under the trustees’ proposed terms. “I support the people of Lazy Point,” but not a 35-year lease, she said. Christopher Carillo, the trustees’ attorney, pointed out that the trustees were not guaranteeing tenants’ ability to obtain a mortgage; rather, they were “providing an opportunity.” Diane McNally, a former longtime clerk of the trustees, raised several points in the draft version of the new lease and urged the trustees to rethink them, warning that they would come to regret the action they are planning to take. A trustee’s term lasts two years and the body’s composition inevitably changes over time, she said. “You are aware you have leases with the Nature Conservancy,” she said. “Are you aware where they are?” She noted that just one trustee nodded.Permits are issued on an annual basis, Ms. McNally said, so that the trustees “have an opportunity to touch base with those utilizing your properties. I encourage you to keep that in mind.” But Rick Whalen of Amagansett, a former attorney for the trustees speaking on his own behalf, supported the proposed lease modification. “This is a community with long standing in the town, founded by people who were not of great financial means,” he said. “I’m in support of the proposal to allow for long-term leases. Thirty-five years sounds reasonable.” The trustees moved to keep the record open for comment through Friday, April 19, and intend to vote on the new lease terms at their next meeting, on April 22.