The web is a powerful tool for researching and buying the perfect present. But what happens when your child sees a banner ad for the toy that will be under the tree in a few days, or the camera you plan to give your husband shows up on your shared Amazon account? The internet can spoil holiday gift surprises for those who share devices.

Dax Hamman knows all too well how ads can reveal too much. About a year ago, he shopped for engagement rings on the laptop he shared with his now-fiancé. "My fiancé saw rings all over my laptop, very much spoiling the surprise," said Mr. Hamman, chief product officer at Chango, a retargeting firm that works with more than 100 of the top 500 internet retailers.

Retargeted ads -- ads that target consumers based on their online history -- have the loosest lips when it comes to gift ideas.

"I passionately believe people show too many retargeted ads," he said, suggesting advertisers stop showing product ads after a purchase is completed. "[Retailers] want to move away from this annoyance of what can almost be referred to as digital stalking."

Glenn Fishback, head of global display at Ebay Enterprise, which does retargeting and manages the e-commerce platform Magento, recommends that retailers stop pushing product ads to consumers 24 hours after they search for a product. This helps maintain the element of surprise, but that's not the main motivation, he said. Consumers are just less likely to convert then.

"Retargeting is like post-it notes; it's that reminder," he said. "What we don't want to do is create wallpaper."

From a technical perspective, it's easy to identify items as gifts and avoid retargeting them, said Chango's Mr. Hamman. But products aren't always flagged that way on the retailer side.

And it's not a top priority for the marketers that give retargeting firms their cues. "It rarely comes up that a client would be thinking about [protecting gift ideas] when it comes to their top-of-mind marketing behavior," said Mollie Spilman, chief revenue officer at Criteo, a retargeting firm.

Amazon, the world's largest online retailer, also blows the whistle on gift ideas. There are benefits to shared accounts, like access to free shipping if you have Amazon Prime. But it leaves your order history out for anyone sharing your device to see. The same is true for other online retailers.

"They think of you as one identity and everything you do gets added into this one notion of identity," said Dave Vronay, CEO and co-founder of Heard, an anonymous social-exchange platform. He said Netflix is an example of how retailers could create different profiles to get over this hurdle. The streaming service allows users to create unique profiles under one account.

Some say it's not the internet's responsibility to keep your secrets. There are many ways to ruin surprises when it comes to gifts, said Ms. Spilman, recalling how she timed her parents shopping trips to guess which stores they went to and checked the closets for presents. "Technology has made it a lot easier, but people are savvy enough to know how to keep things private, just as you keep your personal financial information private."

Of course, there's a difference between hunting for a gift and it popping up when you open a web browser.

For now, it falls on consumers to keep their gift ideas under wraps. And they're getting craftier to keep their secrets -- creating separate Amazon accounts to hide their purchase history, searching for items they have no intention of buying to game the system and fool their gift recipients, or shopping in private browsing mode. Smartphones and tablets are also more private shopping platform, retargeting firms say. They're more customizable, like the Android 5 tablet that allows for multiple accounts, and are shared less often.

"If you're really are looking to be as secretive as possible, you should use your own device," said Ms. Spilman.