At best, advertising is something people tolerate while consuming media. At worst, it’s a turnoff. Media companies engage in a delicate balance between showing audiences enough ads to earn a profit without annoying them so much they leave altogether.

A new study by internet radio service Pandora shows that too many ads can motivate users to pay for an ad-free version, but push many more to listen less or abandon the service. The study found that the additional subscription revenue does not make up for the lost ad revenue from those who listen less or leave the service.

The findings are relevant as digital-media companies seek the proper balance of ad-supported and subscription-supported services. As internet users become more comfortable with paying for digital content, media companies from Netflix and Spotify to newspapers and magazines (including WIRED), are showing that subscription business models may be as attractive as free, ad-supported ones.

“Culturally, we’re moving in the direction of no ads, or at least ad-lite, and it’s a real problem for everyone whose business models are built around advertising,” says Rich Greenfield, managing director and analyst at BTIG. “Our tolerance for our time being ‘wasted’ by untargeted, annoying ads is dropping rapidly because we’re getting more and more options that are ad-lite.”

Greenfield noted that people are more likely to tolerate ads that are highly targeted. That’s worked for Facebook, because the company collects mountains of personal data in order to target ads. But recent criticisms over Facebook’s handling of its 2.2 billion users’ personal data have called that practice into question. COO Sheryl Sandberg told analysts Wednesday that the company has considered other forms of monetization, including paid subscriptions. But CEO Mark Zuckerberg has long said that replacing Facebook’s free model with a paid subscription service would limit the company’s mission of connecting the most people.

Mission aside, it behooves Facebook to remain ad-supported, because that business is extremely profitable. The company reported 46 percent operating margins on $11.8 billion in first quarter revenue. As Bloomberg notes, that equates to roughly $20 per user per year, which would be a steep subscription price for many, particularly in developing countries.

The Pandora study, authored by Jason Huang, a data scientist at Uber; David H. Reiley, an advertising scientist at Pandora; and Nickolai M. Riabov, a senior research scientist at Netflix, supports the notion that advertising is a more profitable path for a digital media company.

The study was not peer-reviewed, as academic studies typically are. Pandora conducted the research itself, as opposed to commissioning the work from independent third party researchers. (Huang and Riabov were interns at Pandora.) The company did not respond to questions about whether it was offered a final edit of the paper. The paper refers to other studies of the subject, but does not present a robust “Literature” section that offers the perspective of previous research, as an academic paper would.

However, its 21-month time frame and scale---almost 35 million users---make it unusual and notable. The authors write that the effects took almost a year to be realized, and a month-long experiment would have underestimated the long-term effects of the increased ads by a factor of three.

The authors divided the Pandora users in the study into nine groups that were served different numbers of ads; some groups received twice as many ads as others. Consistently, the study showed that as the number of ads increased, users listened less. Serving one additional ad per hour resulted in a 2 percent decrease in average listening time and a 1.9 percent decrease in the number of days a user listened. The results were consistent across age groups, even though middle-aged users listen more hours than younger and older ones.