Amid the debate over whether streaming music hurts record labels, artists and the music industry, streaming service Spotify has steadily gained traction, paying out increasingly large sums of money to those labels and artists. Since launching in the US at Fortune’s Brainstorm Tech conference three years ago, the startup has accumulated 40 million users, 10 million of which pay to subscribe to premium accounts.

Spotify has always touted its ability to “make the pie bigger,” meaning, even if record sales fall, Spotify’s increases the amount of money consumers spend on music. To whit: 10 million subscribers who pay $120 a year for Spotify Premium accounts; the average amount of money US consumers of music spent on it during the peak of the CD boom was just $68.

Spotify argues that it helps indie artists get discovered. Pop star Lorde first broke out on Spotify, thanks to some help from the infamous Napster founder and Spotify investor, Sean Parker. Australian rapper Iggy Azalia did as well, and most recently, sing-songwriter Ed Sheeran.

But what about the big artists,which have become the music industry’s last bastion of profits? Recently Taylor Swift, one of the biggest stars in the world, penned a op-ed in the Wall Street Journal, touting her optimism about the future of music. It was both panned and praised: on one hand, it’s easy for a mega-star like Swift to be optimistic. The outlook is good because I can sell records! On the other hand, Swift was smart to recognize the importance of forming direct connections with fans via social media.

But Swift has been slow to embrace streaming. While her songs are available on YouTube, she withheld her last album from Spotify and other streaming services. (It was eventually added to the platform long after the release.)

At Fortune’s Brainstorm Tech conference in Aspen today, Spotify CEO Daniel Ek weighed in on the prickly issue of mega-stars like Swift. “I think she made a lot of great points in her article,” he said, “And there are a few artists that can do totally without giving their music away at all. They don’t need any promotion. They are attracting an audience that will go physically buy their CDs, and Taylor is one of them.”

He noted that ACDC is another example of a company that did great without digital distribution. The band had an exclusive deal with Wal-Mart and sold lots of albums. But that’s not the reality for most artists, he said. “For most artists, they are doing super well by streaming. Ed Sheeran is the best example, he went straight into number one on Spotify.”

Spotify can help promote the “long tail” of indie acts. But doesn’t it need artists like Swift and ACDC to keep fans happy?

“We’re certainly doing everything we can to convince her,” Ek said. “I actually don’t believe that she’d be worse off putting her music up for free as well. There’s no right answer here, and sure there’s some speculation. She can do without free streaming now. But I believe she’d be better of doing it for free. I think if you fast forward three or four years from now, she’ll be on streaming as well.”