Customer satisfaction with auto insurance fell this year from a peak in 2012, but it is still relatively high compared with a decade ago, according to new survey results from J.D. Power & Associates.

Overall satisfaction with auto insurance companies was 794 on a 1,000-point scale, which is 10 fewer points than the same time last year— but the second highest approval since the study was launched in 2000, according to the 2013 U.S. Auto Insurance Study released Monday.

"In 2013, there is a sharp rise in the number of customers who have experienced premium increases," J.D. Power's senior director of global insurance, Jeremy Bowler, said in a prepared statement. "The dollar amount of those increases is also larger, averaging $153 in 2013, compared with an average rate increase of $113 reported in the 2012 study."

When an auto insurer increases rates, customers generally switch more if the increase is between $51 and $100 than if it is less than $50, the survey found. Nine percent of customers switch insurers if the annual rate goes up less than $50, and 18 percent switch if there is an increase between $51 and $100.

"Generally, customers typically have little understanding of how their rates are set by their insurer, or why prices may vary by sometimes hundreds of dollars between companies when they shop for multiple quotes," Bowler said in a prepared statement.

Some companies focus on communicating discounts to strengthen customers' perception of value, Bowler said.

"But the introduction of personal driving data characteristics in establishing discounts, and hence rates, represents another significant step forward for the industry in terms of better communicating price to customers," he said.

On average, customers in New England were the least satisfied among regions of the U.S.

Average approval numbers — the bigger number, the more satisfied — were: 769 in New England; 776 in New York; 792 in the northwestern U.S.; 797 in the north-central U.S. (Midwest); 801 in central U.S.; 802 in Mid-Atlantic; 804 in the southeastern U.S.; 805 in the southwestern U.S.

In New England, Amica Mutual had the top score for customer satisfaction with 850. Other companies that received better-than-average satisfaction were: GEICO, 794; State Farm, 794; The Hartford, 793; Nationwide, 787; Liberty Mutual, 782; Allstate, 781; and Progressive, 775.

Companies below the New England average satisfaction were: Arbella, 755; Plymouth Rock Assurance, 752; The Hanover, 749; MAPFRE-Commerce Insurance, 748; MetLife, 744; Travelers, 744; and Safety Insurance, 740.

Results from last year don't compare perfectly with this year because New York was included with New England as the Northeast region. Nevertheless, Amica Mutual has been the top rated auto insurer in the region.

The survey was conducted between March 15 and April 17, with 45,521 surveyed nationwide, including 4,275 in New England.

Approval rating among those who have USAA, special insurance available only to members of the military and their families, was 898, but it is an outlier because it's not available to the general public.