When the Golden Rule Insurance Company rejected her application for health coverage last year, Peggy Robertson was mystified.

“It made no sense,” said Ms. Robertson, 39, who lives in Centennial, Colo. “I’m in perfect health.”

She was turned down because she had given birth by Caesarean section. Having the operation once increases the odds that it will be performed again, and if she became pregnant and needed another Caesarean, Golden Rule did not want to pay for it. A letter from the company explained that if she had been sterilized after the Caesarean, or if she were over 40 and had given birth two or more years before applying, she might have qualified.

Ms. Robertson had been shopping around for individual health insurance, the kind that people buy on their own. She already had insurance but was looking for a better rate. After being rejected by Golden Rule, she kept her existing coverage.

With individual insurance, unlike the group coverage usually sponsored by employers, insurance companies in many states are free to pick and choose the people and conditions they cover, and base the price on a person’s medical history. Sometimes, a past Caesarean means higher premiums.