The Democrat-controlled General Assembly won’t be returning next week to override any of Democratic Gov. Dannel P. Malloy’s six vetoes.

Democratic leaders in the legislature decided not to wage a war with the first Democratic governor in 20 years over six pieces of legislation, even though they say they’re still trying to work out a deal on at least one of them.

House Speaker Chris Donovan, D-Meriden, said there’s some bills of concern and he’s still working with his caucus and members of the governor’s office to see where things stand. But he acknowledged it was unlikely the legislature will return to override a gubernatorial veto.

Sen. President Donald Williams, D-Brooklyn, said they’re working with healthcare advocates and the governor’s office to see if they can’t find a middle ground on a bill that would have required the state Insurance Commissioner to hold a public hearing on any health insurance rate increase over 10 percent.

He said they’re trying to figure out how to create some forum or discussion of rate increases that are out of line with medical claims history or actuarial data.

Earlier this month Malloy said he vetoed the bill because it would create a costly and unnecessary requirement.

“The department regularly rejects requests that are not actuarially warranted,” he said in his veto message. “The current process fully protects from excessive and discriminatory rate increases.”

But proponents of the bill questioned that assertion.

“I know of only two instances in the past five years or so when a health insurance rate was rejected, and both times, it was due to the involvement of the attorney general and healthcare advocate,” Jennifer Jaff, executive director of Advocacy for Patients with Chronic Illness Inc., said the day Malloy vetoed the bill. “I do not believe that we can get a grip on escalating health insurance premiums in Connecticut without public hearings.”

Under an agreement reached between the executive and legislative branches, the Office of Health Advocate can request that the Insurance Commissioner hold a hearing for rate increases of at least 15 percent or more on individual and small group HMO plans.

The collaboration allows for up to four hearings a year while the commissioner can exercise his current broad statutory authority to hold hearings on other health products, including long term health care policies, if necessary. Additional changes could be discussed next year, according to a press release from Williams’ office.

“Disagreement over the specifics of certain legislation is inevitable, but fortunately we all agree that there must be greater transparency in the rate approval process,” said Sen. Majority Leader Martin Looney, D-New Haven. “I’m pleased that we’ve been able to work with the Malloy Administration and begin work on a compromise that will benefit consumers and enhance close scrutiny of proposed health insurance increases.”

The five other bills Malloy vetoed included An Act Reconstituting the Connecticut Capitol Center Commission, An Act Promoting Economic Development In The Area Surrounding Oxford Airport, An Act Concerning Revisions of Municipal Charters, An Act Concerning Exempting Certified Police Officers From Telecommunicator Training, and An Act Concerning the Siting Council.