In the wake of data breach problems at social media giant Facebook Inc. and the emergence of other online threats, U.S. consumers are understandably wary of how online marketers might violate their privacy. But most also value exclusive offers—such as military or teachers’ discounts and other targeted promotions that require a shopper’s personal information—when they can get them.

A survey of 1,023 American adults from verification company SheerID and conducted by market research and strategy firm Kelton Global found a plurality of consumers like offers they can sign up for. Of respondents, 40% say they prefer to opt in to such offers via an online form on a brand’s website, while just 17% of consumers surveyed preferred that brands use their activity on a website. Other means of verification were far less popular:

“Consumers are OK about giving up their personal data if they are getting a special offer,” says Sai Koppala, chief marketing officer at SheerID. But he added that marketers risk creating a “creepiness factor” if they use data not explicitly supplied by the consumer—such as information gleaned from social media or via web cookies, which are small bits of data placed on a visitor’s computer, usually to help websites remember information about the visitor.

The survey found that 73% of consumers believe brands use personal information without their knowledge when verifying them for a special offer. In addition, 83% of those surveyed said they would be concerned about how the information used to qualify them would be used. Top data-use concerns were the possibility that the personal information would be shared (mentioned by 62% of those concerned), who might access the information (59%), the potential for the information to be used without their consent (56%) and the security of the information collected (51%).

Despite their concerns, a strong majority (68%) say exclusive offers are more valuable to them than traditional coupons that are available to everyone, and 94% U.S. consumers would take advantage of an exclusive offer not typically offered to the general public. And consumers are willing to provide at least some basic information in order to take advantage of those offers. Among the items consumers say they are “extremely willing” to share in order to get a special offer are e-mail address (37%), full name (36%) and date of birth (27%).

The survey also showed that an exclusive deal can elicit an emotional response by consumers. Asked to identify words that describe how a special offer would make them feel, 54% of respondents selected “rewarded” and 47% chose “excited” and 36% picked “special.”

Consumers surveyed also admitted a willingness to cheat in order to get a special offer. The survey found that 24% redeemed an exclusive offer when they knew they didn’t qualify for it. Among those who did that, 49% used a code or link forwarded to them by somebody else.

Millennials (48%) are around twice as likely as Gen Xers (23%) to have wrongfully redeemed an exclusive offer and nearly seven-times as likely as consumers who are Baby Boomers or older (7%).

Asked which offers they prefer to get, most of those surveyed prefer some kind of discount on the purchase itself, as opposed to free shipping, a future free gift or other kinds of perks. The most popular kind of offer is a 25% one-time discount on the shopper’s current purchase.