Amazon’s video servers are working a lot harder these days. Amazon Video has now become the third-largest source of peak internet traffic in North America, behind longtime leaders Netflix and YouTube, according to new research by traffic analysis firm Sandvine.

Amazon Video’s climb to third place has been rapid. Three years ago, it wasn’t even placing consistently in the top 10. Today, it accounts for 4.3% of what the tech industry would refer to as peak downstream traffic on fixed-access networks—which is basically people streaming video at home.

Netflix has long been the dominant source of US peak-time internet traffic. In 2012, it made up a fifth of downstream peak-time traffic. That figure has grown steadily over the years; it now accounts for 35% of peak downstream traffic. YouTube has played second fiddle consistently. This year it was responsible for 17% of peak downstream traffic.

Amazon Video’s rapid rise means that it’s now solidly in third place, ahead of the usual contenders for that spot, iTunes and BitTorrent. While iTunes’ traffic share has been relatively stable over the years, usually weighing in at around the 3% mark, BitTorrent has suffered a steep decline. In 2008, the file-sharing system accounted for nearly a third of all peak-time traffic, according to Sandvine. Its share of that traffic is less than 3% this year.

Amazon is driving video growth by successfully bundling it with Prime. Estimates from Bernstein, the investment research firm, suggest that about 80% of Prime subscribers in the US also take up Amazon on its video offering, which used to be accessible only as part of a bundle with the loyalty program.

Amazon’s seamless cross-selling of its Prime services and video is clearly working. Bernstein, a noted Amazon bull, believes that the company is laying the foundation for a full-blown Netflix competitor in the years to come. Even BitTorrent seems to be learning that with video, convenience trumps everything else. It’s launching a new streaming app to try to claw back relevance in a market that’s getting used to video served by the Netflix-Google-Amazon triumvirate.