Two months ago, the state Division of Insurance rejected 235 proposed premium increases that would have taken effect April 1, requiring insurance companies to continue billing customers at 2009 rates. The new round of proposed increases, submitted this week, covers health plans coming up for renewal in the three-month period that starts July 1.

Blue Cross Blue Shield of Massachusetts, the state’s biggest health insurer, is requesting increases averaging 12 percent, on the lower end of the range it submitted earlier in the spring. Harvard Pilgrim Health Care, the number two carrier, wants increases that range from 8.8 percent to 11.9 percent, about the same range it sought in the round that was rejected.

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