By Joe Flint

When ViacomCBS Inc. unveiled plans last week to launch Paramount+, a supersize streaming service featuring content from across the media company's myriad units, something was missing: Showtime.

The omission set off a round of speculation about the fate of the premium network, best known for well-regarded dramas such as "Homeland" and "Ray Donovan." Some observers viewed the move as a lack of confidence in a service that has toiled in the shadow of much-bigger rival HBO and competes in a crowded environment that includes rivals Netflix, Hulu and Amazon Prime Video.

"We have urged them to sell this asset to someone else," said Michael Nathanson, media analyst and founding partner at MoffettNathanson.

Don't bet on that, says ViacomCBS Chief Executive Bob Bakish, who holds that the network, with its mix of original shows, movies and boxing, is strong enough to stand on its own.

"Showtime is not thought of as a leader in premium, but it is leading this year," Mr. Bakish said in an interview. Showtime's direct-to-consumer streaming offering, also called Showtime, gained more subscribers in the first six months of this year than it had in the previous three years, he said.

ViacomCBS doesn't break out subscribers for Showtime -- which is available as an add-on channel on cable or through the streaming platform -- but people familiar with the operation say it has 27 million subscribers, seven million of whom are coming through the Showtime streaming service. Credit Suisse expects that number to top nine million next year.

Those numbers still pale in comparison to HBO and Netflix, which respectively have 36 million and 60 million subscribers in the U.S. The size of the gap has prompted some media analysts to question Showtime's long-term value to ViacomCBS.

Mr. Nathanson said Showtime "is on a very modest revenue growth trajectory," adding that he doubts the network can spend at a level to compete with its rivals.

"I think we're a little bit underestimated," Showtime CEO David Nevins said in an interview.

Mr. Bakish said some of Showtime's streaming growth can be attributed to people staying at home during the coronavirus pandemic and buying additional content, but that ratings for all versions of the service have been solid.

Showtime got strong performances from the final seasons of the spy drama "Homeland" and the Hollywood detective serial "Ray Donovan." Newer dramas including the high-finance soap "Billions" and urban drama "The Chi" have also been solid. The network also has unscripted fare, such as the late-night talk show "Desus & Mero."

Showtime has also benefited from the surge in new streaming services that might have overwhelmed and confused consumers, Mr. Nevins said. "Our competition becomes a little diluted in their brands," he said, alluding to the fact that HBO was briefly available on three separately branded streaming platforms: HBO Now, HBO Go and HBO Max.

Showtime's streaming growth comes at a critical time for ViacomCBS. Revenue was down 22% in the company's most recent quarter, in large part because advertisers are cutting spending during the pandemic. Theatrical revenue was nonexistent for the same reason. Showtime's streaming subscribers are more profitable to ViacomCBS than cable and satellite subscribers because more of the revenue goes directly to the network.

Mr. Nevins said Showtime's willingness to form partnerships with all distributors gives it another edge. New streaming service HBO Max hasn't been able to reach agreements to be distributed via Roku and Amazon's streaming devices, and NBCUniversal's Peacock doesn't have a deal with Amazon. Showtime is available everywhere.

"We're a pure-play content company," Mr. Nevins said. "We have a flexibility other people don't have that gives us a competitive advantage." Unlike HBO Max, which is owned by AT&T Inc., and Peacock, a property of cable operator Comcast Corp., "we have no ulterior motives to support a distribution system" that complicates relationships with third parties, he said.

ViacomCBS was also the first programmer to cut a deal with Apple Inc.'s new Apple TV+ streaming service, which is now selling access to Showtime as part of its own content offering.

Showtime has been acquiring more documentaries and nonfiction programs, both because of their popularity and to keep fresh content available as the coronavirus slows the production of scripted fare.

Although some veteran Showtime programs such as "Homeland" and "Ray Donovan" ended recently, "Billions" and "The Chi" are still in their prime. The hit "Shameless" -- about an extremely dysfunctional family -- will be back later this fall and a new limited series about the relationship between President Trump and former Federal Bureau of Investigation Director James Comey -- starring Jeff Daniels as Mr. Comey -- is scheduled to make its debut next week. On top of that, Bryan Cranston of "Breaking Bad" fame is starring in a legal thriller called "Your Honor" set to premiere later this year.

Write to Joe Flint at joe.flint@wsj.com