Indeed, Islamic State-affiliated accounts have spread violent images, propaganda videos, and calls to action online. But their influence is waning.

Berger and Perez determined that there’s usually an average of only 1,000 easily discoverable English-speaking terrorist accounts at a time, and that the average Islamic State supporter has only 300 to 400 followers. And those accounts appear to be stuck in an echo chamber: They generally only interact with other supporters, rather than spreading their message to new followers.

The researchers monitored a list of ISIS supporters’ accounts—maintained by hand by a particularly active supporter—for a period of nearly four months in 2015, making note of account suspensions and new additions to the list.

At times, Twitter suspended the list members’ accounts at a high pace, sometimes even suspending a user multiple times in one day. But most of the time, only about 2 percent of the list was suspended every day.

Berger has long railed against the “whack-a-mole” thesis of Twitter takedowns—the idea that suspending an online account is a waste of time because new accounts will quickly sprout up to take the place of a deleted one. To test that theory, he and Perez tracked four users as they were repeatedly suspended by Twitter and reemerged every time with a different name.

“We found suspensions typically had a very significant detrimental effect on these repeat offenders, shrinking both the size of their networks and the pace of their activity,” the researchers wrote. “Returning accounts rarely reached their previous heights, even when the pressure of suspension was removed.”

Twitter has further accelerated the pace of its account removals in the months after the researchers’ study period. Just a few weeks ago, the company announced that it has taken down 125,000 terrorist-related accounts since mid-2015. The company also said that staffing increases had led to quicker takedowns.

But a few lawmakers have repeatedly pushed for legislation that would require social-media companies like Twitter and Facebook to do more. A bill from Richard Burr and Dianne Feinstein, the chairman and vice-chair of the Senate Intelligence Committee, would require the platforms to report terrorist activity on their networks to law enforcement. But concerns about freedom-of-speech violations and the potential loss of valuable intelligence from terrorists on Twitter has led opponents in and out of the Senate to speak out against the proposal.

If Twitter can show that its own increasingly aggressive campaigns to stomp out propaganda are working, perhaps it can dodge a legislative intervention—one that would burden social-media companies with heavy reporting duties and bring another platform under government surveillance.