Advocates for a stronger rent control policy dominated the Boston City Council’s second public hearing on the issue Thursday, ratcheting up pressure to alter the controversial plan put forward last month by Mayor Michelle Wu.

Wu has repeatedly defended her proposal as balanced. It would cap annual rent increases at a maximum of 10% in high inflation years, and the rate of inflation plus 6% in most other years. Her rent control plan would also exempt recently constructed buildings for 15 years, as well as landlords who own six units or fewer and live on-site with their tenants.

Thursday’s commenters insisted the mayor's proposal be tightened to counter a rising tide of unaffordability by shortening the building exemption period and lowering the annual rent increase cap to a maximum of 5%.

“We’re asking for just rents,” East Boston resident Maribel Castro said through an interpreter.

Castro said she is currently trying to cope with a rent increase brought on by a new landlord seeking $3,000 a month for a two-bedroom apartment.

“And that’s not fair. … We’re asking Michelle Wu, the mayor, to do something about it [and] also all of you,” she said to the sitting councilors.

James Cordero, a public school teacher and Dorchester resident, asked the council to “refine” the rent control policy to ensure more renters are protected.

“That means this 10% cap really should be reduced to a 5% cap including inflation … and we really need to make sure that this policy applies to as many properties as possible, including those properties that are new construction,” Cordero said.

Natalie Bell, a Dorchester homeowner, testified that her ability to purchase a home was “only made possible” through her partner’s access to generational wealth.

“Our housing cost … is about one half of the market rate I see for comparable rental units,” she said.

“Why is 6% plus inflation even being called 'rent control' at all? It sounds kind of like profit allowance," Bell said. "I want to close by asking if you can imagine legislating that the wage of every renter in the city would also go up 6% plus inflation, because if we can’t picture that happening, then we should grapple with what is happening, which is that we’re privileging an investor class at the expense of everyone else.”

Until now, the criticism of Wu's rent control plan came principally from organized interests such as the Greater Boston Real Estate Board, which launched a $400,000 public campaign against the policy, and MassLandlords, which recently filed a lawsuit seeking documents related to how Wu chose the members of her rent control advisory committee.

The hearing came after repeated rallies across the state in support of a lower cap on annual rent increases. In January, advocates gathered in front of the State House, insisting that a 5% maximum would keep rental rates stable and be more in line with stagnant wages.

Last week, at the City Council’s first hearing on Wu’s proposed policy, councilors began signaling ways they might attempt to change the plan.

At Thursday's public hearing, several councilors applauded Wu’s effort to initiate public discussion on a wedge issue and indicated a desire to amend her proposal.

“This is a historic moment, yes,” said Councilor Kendra Lara, who has publicly stated she wants the rental cap lowered. “And I want to commend Mayor Wu for being able to take the step to take the step to even put this on the floor in front of us — but what good is a historic moment if we’re going to squander it?”

“One question I’m just wondering about [is] how we ended up at CPI plus 6%,” said Councilor Liz Breadon.

Breadon added: “I really applaud Mayor Wu … but, I feel that we need to really scrutinize the numbers a bit more to see if we can improve the situation.”

Councilor Ricardo Arroyo cited census data that shows Boston has already lost thousands of Black residents in the past couple decades.

“I have no doubt that that has to do with the cost of living. ... So I think this is an incredibly important step to do this for rent stabilization,” he said, “and I recognize that for people who have already been displaced, this comes too late.”

Councilor Brian Worrell echoed concerns expressed by small landlords including a need for increased rental assistance and the need for housing production “on top of” a rent control policy.

Councilor Kenzie Bok echoed Wu's assertion that the proposal on the table balances the interests of renters and housing creators.

Councilors are scheduled to hold a technical session to begin proposing adjustments to the policy next week.