I eventually prevailed and got the refinancing.

But around that time, I got the renewal letter for the homeowner’s insurance on our house in Connecticut and was shocked to see that it was being insured for a value 14 percent higher than we paid in 2008. I know homeowner’s insurance is meant to cover the cost of replacing the house, but the price we paid for our home in 2008 was not just for the house but included the yard, the street where we live, the property taxes, the schools and other intangibles. And the price I could get for the house now is less than I paid back then. So why the high appraisal?

The question isn’t a new one. After all, appraisals seemed to be just as subjective when the market was moving up. Why is the process so opaque? I set out to try to figure that out. Here are a few things I’ve found that can improve the outcome, though I can’t promise that you’ll be entirely satisfied.

SELLING AND BUYING One component of selling a home has always been gauging the emotion of a prospective buyer. But several brokers told me that buyers and sellers who need financing for a home should be concentrating instead on the temperament of the bank lending the money.

“Over the past two years, houses are not worth what the owners want or what the buyers will pay for them,” said Peggy Bates, a broker with William Pitt Sotheby’s International Realty in Stamford, Conn. “A house is worth what the appraiser says it is.”

She says she makes prospective clients have their house appraised before she will list it. If they insist on determining their own value, she said, she makes them sign an agreement to drop the price in four weeks if the house does not sell.