"I'm the first to acknowledge that it is time for us to contract and there is political pressure for us to contract," said Carlos Lacasa, chairman of the Citizens board and a former state legislator from Miami.

Lacasa and other members of the Citizens board said they want lawmakers to  reconsider a controversial bill from this past year that would allow Citizens to raise its rates more than 10 percent a year and would make it harder for policyholders to be covered by Citizens.

For example, state law now says that a homeowner is eligible for a policy from Citizens if the only alternative is a policy from a private company charging rates that are 15 percent higher. The new proposal would make homeowners ineligible for Citizens unless a private company is charging rates 25 percent higher.

Citizens officials also began discussing changes that could be done without  approval from the Florida Legislature, including increasing deductibles for sinkhole coverage and eliminating certain types of coverage.

One proposal that was discussed would require homeowners to pay 10 percent of  the cost of any sinkhole damage before the insurance coverage kicks in.

Such changes could get a rough reception in the Florida Capitol.

Some GOP legislators have already signaled that they are not anxious to consider any major property insurance changes during 2012. The Florida Legislature approved a comprehensive property insurance bill earlier this year only to see it trigger protests when Citizens tried to enact large rate hikes for sinkhole coverage.

Sen. Mike Fasano, R-New Port Richey, said proposed changes to Citizens would not shrink the size of the insurer because private companies don't want to cover  people in places such as the Tampa Bay area where the majority of sinkhole claims have been.

He called private insurers "hypocrites" who won't start offering coverage to  homeowners regardless of what the state does.

"People in the Tampa Bay area would love to have a choice, they don't have  one," Fasano said. "Our governor and a few others in Tallahassee don't get  it."

Some members of the Citizens board expressed a similar fear on Monday. But  John Rollins, a board member and an insurance actuary contended that new  statewide data shows that many carriers are adding policies, just not in the  Tampa Bay area or in South Florida.