Mr. Rosenberg says, “Once the novelty has worn off, consumers are not going to dive for their phones just to start an app to get info about the ad they’ve just seen.”

Last year, Nielsen released a study it did for Google in which subjects were shown a 15-second commercial for a sports sedan. Of those who saw the ad only on television, half were able to recall the name of the manufacturer. Of those who saw it at different times on four screens — television, computer, smartphone and tablet — about three-quarters remembered the name.

Perhaps most surprising, however, was that even after the message was pounded in four different ways, some 26 percent didn’t recall the advertiser.

Marc DeBevoise, senior vice president and general manager of CBS Interactive’s entertainment division, seems wary of supplying the second screen with content that distracts from the main one.

“Extensions”— his term for complementary content — “are rarely meant to be watched or used at the same time that the show is watched,” he says. “They’re meant to bridge the gaps between watchings.”

So far, second-screen apps are dwarfed by the popularity of the social media giants Facebook and Twitter. “Television is social,” says Elizabeth Shaw, an analyst at Forrester Research. “We’ve always talked offline with others about what is going on in our favorite shows. Now it’s moved online. Networks know this and are trying to figure out how to move these conversations to their own Web and mobile properties.”

MR. DeBEVOISE says that “we do think social commenting during shows is a big opportunity,” citing the 13 million “social media comments” counted by Bluefin Labs during the CBS broadcast of the Grammy Awards last month. Bluefin says the number was a record for any program it has tracked.