(HealthDay News) – Many Americans say they’d submit to insurance company medical tests and lifestyle monitoring in exchange for lower-cost premiums, a new Harris/HealthDay poll finds.

The poll of more than 2,000 U.S. adults found that a majority would be “very willing” to have various tests and share the results with their health insurer — provided there was a financial incentive, such as a lower monthly premium or smaller co-pays. Many were even open to intrusive measures. Just over half said they’d agree to let their health plan monitor any exercise regimen they were using to lose excess pounds or control diabetes. What’s more, nearly half said they’d undergo genetic tests to gauge their risks of “cancer or inherited medical conditions.”

“You have to wonder to what extent people understand the implications of that,” Jennifer Blumenthal-Barby, an assistant professor of medicine and medical ethics at Baylor College of Medicine in Houston, told HealthDay. Privacy has been a long-time concern with genetic testing, because employers or insurers could potentially discriminate against people at increased risk of a given disease.

In recent years, many U.S. companies that provide health insurance have started offering financial incentives. Workers who undergo blood pressure, cholesterol, or blood sugar tests, or who join an exercise or disease-management program, can get a break on what they pay into their insurance. Some employers also base the financial reward on the results of those tests. In the Harris/HealthDay poll, most people were open to those simpler types of tests. “This survey shows that there is a substantial opportunity for health plans to test and monitor the health status and health risk behaviors of health plan members, but that they would have to be extremely careful to avoid a potentially explosive backlash,” said Harris Poll chairman Humphrey Taylor.

The complete findings of the newest joint Harris/HealthDay poll are available here.