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Still, the approach stirs privacy concerns.

“Anytime you’ve got that data somewhere, it can be accessed,” said Traci Stewart, as she was taking a smoke break in downtown Indianapolis on a recent Friday. Stewart, 40, said she would worry that her health insurance costs would rise because she smokes.

Last year, Indiana University _ which has more than 17,000 full-time employees _ offered three ways for workers to ease a cost increase for their benefits plans. They could complete a heath assessment, do biometric screening and sign an affidavit stating that they would not use tobacco or that they agreed to enroll in a smoking cessation class.

The assessment, in particular, drew criticism, said math professor David Fisher, one of the sponsors of the employee petition. He noted that it included a question about religious service attendance.

“They sort of seemed to have gone the extra mile to try to offend as many people as they possibly could,” he said.

IU Chief Financial Officer Neil Theobald said in an e-mail that the assessment’s questions aimed to gauge an employee’s “support structures.” He decided to drop it after seeing the controversy it stirred, but the university kept the other programs.

James Ventress, 40, of Indianapolis, said he would have no privacy worries if his employer offered to trade a premium break for a health assessment. He said the screenings would help workers learn about their health.

“It’d help me out if they paid for it,” said Ventress, who installs floor coverings.

Benefits experts expect more employers to offer discounts for workers who agree to disclose health habits.

“We can talk about this being a cost-control issue, and it is. But the larger social issue is … we have a population that’s really unhealthy, and employers are in the vanguard of trying to engage people in getting healthier,” Towers Watson’s Abbott said. “Employers are insisting on greater accountability for personal health improvement.”