Discovery Channel founder John Hendricks is tweaking the business model for his video streaming startup after falling short of his initial expectations for subscriber growth.

When CuriosityStream was launched in 2015, Mr. Hendricks predicted that between five million and seven million people would pay to view the company’s blend of documentaries and other non-fiction content within two to five years.

Three years in, the cable pioneer has managed to sign up one million subscribers, suggesting a need to change course.

“When we launched Discovery back in the infancy of the cable industry, the lessons we learned during our first few years of operation were huge contributors to our future success,” Mr. Hendricks said. “You evolve, you adjust, you stay nimble.”

CuriosityStream’s new business model calls for a free version of the service — “CuriosityStream Showcase” — to be supported by advertising. Ultimately, CuriosityStream is seeking advertising deals with six sponsors at a time, totaling eight figures. The sponsorship arrangement includes an unskippable, 15-second ad that will run before each video, and branding around each video. The first sponsorship, with Sprint, went live this morning.

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CuriosityStream is also rolling out lower-priced subscription packages. Previously, the company charged $5.99 per month for high-definition video and $11.99 per month for 4K definition. Now, high-definition video will be $2.99 per month, with 4K playback available for $9.99.

The business model pivot is rooted in the spending habits of streaming subscribers, Mr. Hendricks said. The company has concluded that consumers only spend about $30 per month on streaming-video services. Much of that money goes toward premium movie and TV services like Netflix, Amazon Prime and Hulu, leaving little budget leftover for additional subscriptions.

CuriosityStream has made some progress toward its subscriber goals. Three years in, the company has drawn nearly 1 million subscribers. Roughly three-quarters of those subscribers come from third-parties — cable system operators and other video providers who pay CuriosityStream to provide its service to their customers. The rest subscribe to CuriosityStream directly.

Mr. Hendricks wants to increase the proportion of people who subscribe directly to CuriosityStream because the company keeps all of the revenue from direct subscriptions but shares a portion of revenue with distribution partners, he said. However, third-party providers are useful because they expose a large swath of potential subscribers to CuriosityStream’s content. He hopes to reach between 1.5 million and 2 million subscribers by the end of the year.

Mr. Hendricks was not alone in predicting that the rise of cord-cutting would create a broad subscriber base that could be tapped by incipient streaming firms. Seeso, a streaming service launched by Comcast Corp’s . NBCUniversal in 2016, hoped to lure comedy lovers before shutting down in 2017.

CuriosityStream is focused on acquiring and producing non-fiction programming for a fraction of the cost that companies like Netflix Inc. and Amazon.com Inc. spend creating their original content. Whereas those companies spend billions on content annually, CuriosityStream plans to spend about $30 million for programming in 2019.

So far, Mr. Hendricks has not sought money from venture investors to fund CuriosityStream. He has personally invested $60 million since March 2015 and raised an additional $30 million in debt financing. Eventually, the company will seek additional investment, he said.

By 2023, Mr. Hendricks predicts, the growing adoption of high-speed internet around the world will create a potential consumer base of 1.5 billion video streaming subscribers. Mr. Hendricks projects a market size of about 40 million CuriosityStream customers if between 2% and 3% of those high-speed internet users subscribe.

“A couple of years ago, it was huge news that there were three billion people on the planet that were connected to the internet,” Mr. Hendricks said. “That’s up to four billion now.”