Roughly one million customers of the Citizens Property Insurance Corp. will see a 10 percent increase on their premiums Jan. 1.

The board that oversees the state-backed insurer approved the increase Wednesday. However, the governing board backed off a plan to reject rate cuts for customers in some parts of the state after some heated debate and input from the Office of Insurance Regulation. The board voted to cap any cut at 10 percent.

Some 80,000 Citizens customers are eligible for a lower rate on their premium based on new rate models.