Facebook received a flurry of criticism earlier this week when it said that it would allow graphic videos of beheadings to remain posted on the site so long as the user who posted it was “condemning” the violence. Everyone from professional media experts to British Prime Minister David Cameron weighed in on the issue and called on Facebook to update their policy. Perhaps feeling the pressure, Facebook announced on Tuesday that it would update its stance on violent videos and tighten its rules about their posting.

“As part of our effort to combat the glorification of violence on Facebook, we are strengthening the enforcement of our policies,” Facebook said in a blog post. “First, when we review content that is reported to us, we will take a more holistic look at the context surrounding a violent image or video, and will remove content that celebrates violence. Second, we will consider whether the person posting the content is sharing it responsibly, such as accompanying the video or image with a warning and sharing it with an age-appropriate audience.”

Though Facebook’s policy change has been hailed as a victory, with Prime Minister Cameron tweeting that he was “pleased” with the updated rule, Facebook hasn’t actually changed its position much. It will still allow graphic videos to be posted, but will simply place a greater emphasis on warning users about violent content. That’s a step in the right direction, but for people concerned about children seeing these videos, it likely won’t be enough to stop them from clicking through.