Verizon Wireless says it will soon allow customers to sidestep the mysterious “perma-cookie” it has placed on at least some phones to track user behavior and help target ads.

According to The New York Times, the company will give users the ability to completely refuse the tracking enabled by the cookie. Called the Unique Identifier Header, or UIDH, the little serial-number-like string of data is inserted into unencrypted web traffic, slipped into smartphones that surf the net via the carrier’s cellular and data network, and is virtually undeletable.

The digital marker, which is viewable by any website a user visits, is meant to be a tool central to the wireless carrier’s internet advertising business. But critics and privacy advocates point out that it could give marketers a way to build elaborate profiles of everything we do online. Recently, it emerged that U.S. carrier AT&T is using a perma-cookie, too.

The decision to let Verizon’s 123 million subscribers opt out of the program comes in the wake of increasing pressure from consumer advocacy groups. Earlier this week, The Times reports, the nonprofit group Consumer Watchdog called on federal regulators to impose tough rules on wireless carriers that would prevent them from sharing information on customers for marketing purposes.

In a similar effort, this month the Electronic Frontier Foundation, a San Francisco-based digital rights group, started a petition asking federal agencies to penalize Verizon for failing to disclose their ad-tracking practices to consumers. The petition got over 2,000 signatures.

Letting Verizon’s users have the option to stop the tracking is a small win for privacy advocates. But, as an EFF staff lawyer astutely pointed out to the Times, the better policy would be making the carrier’s tracking program opt-in, instead of opt-out, from the very beginning. Additionally, cybersecurity experts have told the Times that Verizon likely doesn’t have a way to prevent third parties from hijacking its perma-cookie for their own purposes.​