HBO, Showtime, and Sony Corp. are jumping into online television. But instead of putting their Web traffic on the public Internet’s main thoroughfare, they want to be in a separate lane that would ensure their content gets special treatment.

Those companies have talked to major broadband providers such as Comcast Corp. about having their Web TV services treated as “managed” services, according to people familiar with the discussions. In effect, that would move them away from the congestion of the Internet, which they fear will only get worse as more people opt to stream movies and TV shows on the Web.

The other benefit: A separate lane would be exempt from monthly data-usage thresholds operators enforce for public Internet traffic, saving customers from the surcharges that can kick in if they binge on too many episodes of “Game of Thrones” or “Homeland.”

Such arrangements would tap into a gray area of the debate over “net neutrality,” the principle that all traffic on the Internet should be treated equally.

The Federal Communications Commission’s recently approved net-neutrality rules, which go into effect in a few months, bar broadband providers from accepting payment from companies to favor their traffic. And the rules say the FCC “expressly reserves the authority to take action” if it finds that specialized services are “being used to evade the open Internet rules.”