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Yesterday, HBO announced plans to sell Web video subscriptions. Today, CBS.

CBS?

Yup, CBS. The broadcaster is also getting into the digital video subscription business, with an offering that will let users watch almost any show it airs, live or on demand, on a variety of devices.

And like the HBO plan, this one doesn’t require users to have a traditional pay-TV subscription: All you need is an Internet connection and $6 a month.

But there are several big differences between CBS’s Web video service and the one HBO talked about yesterday.

For starters, CBS is selling access to shows that are technically available for free to anyone with a broadcast antenna. And unlike HBO’s service, this one isn’t theoretical: CBS is selling “CBS All Access” right now, via its CBS.com site and its mobile apps.

Think of the service as part Hulu, part Aereo, with tweaks: Like Hulu, the service powered by CBS competitors Fox, NBC and ABC, CBS All Access will give viewers a big library of old shows, as well as ones that have appeared as recently as the night before.

And like Aereo, the startup CBS successfully sued, CBS All Access will let viewers stream shows live, via the Web, to phones, tablets and computers.

The live streams are designed to be counted by Nielsen, and will run with the same ads that appear on regular TV. Some of the newer on-demand shows will also have ads, though for now CBS says it will cut down the frequency of those spots by 25 percent. Shows that are no longer on the air will run ad-free.

Like most digital media offerings, the service also comes with gaps and caveats. The biggest one is that the service can’t show the NFL games that CBS broadcasts on Sunday afternoons and Thursday nights, because it doesn’t have streaming rights to those.

For now, the shows CBS will livestream are only available in the 14 cities where CBS owns the local CBS station, including New York City, Los Angeles and Chicago. And the depth of CBS’s on-demand access to recent shows varies depending on whether it owns the program it aired, or if an outside studio like Warner Bros. made the show.

Still, the announcement is fascinating, especially coupled with HBO’s plans. All of a sudden it looks like the TV Industrial Complex, which appeared immovable for years, may be morphing quickly: Away from big bundles of networks and toward more nimble plans that let viewers assemble the networks they really value — or at least smaller bundles of them.

Note that both HBO and CBS say that’s not what they’re trying to do: Both insist, with good reason, that they like the current setup, where they wholesale their programs to pay-TV operators like Comcast.*

And in CBS’s case, where the network is able to command a big monthly fee for each video subscriber a pay-TV company has whether they watch the network or not, things are particularly sweet.

“This isn’t a shot across the bow” of the cable providers, CBS CEO Les Moonves said in an interview. Still, he notes, as distributors consolidate and gain more negotiating leverage, the ability to sell its programming directly to consumers, without requiring any help from the likes of Comcast, is useful for CBS.

Moonves also notes that he’s considering an HBO-like move for Showtime, his own pay-TV network. “We’re talking about it,” he said. “We’re obviously getting the technical capabilities ready.”

The audience for the service Moonves is launching today seems limited, since anyone with a pay-TV subscription already gets CBS shows. The network’s audience also skews older than its rivals, which means its viewers are the least likely to watch shows anywhere but on a traditional TV set, live.

That reduces its potential customer base to a few different pools: People who value the ability to watch stuff live on mobile devices, people who don’t have pay-TV subscriptions or broadcast antennas and people who really, really like some of CBS’s shows.

CBS executives won’t use the word “niche” to describe the service’s appeal. “It’s about super-fans being able to get a lot more of our content,” Moonves said.

Still, Hulu’s Hulu Plus service sells access to network TV shows — though not live ones — for $8 a month, and it has more than six million subscribers.

Even a third of that audience would generate $144 million a year, at what would likely be a very generous margin. And unlike Hulu, CBS would keep all of that money for itself.

* Comcast owns NBCUniversal, which is a minority investor in Revere Digital, Re/code’s parent company.