WALT DISNEY CO. is stepping up its fight with Netflix Inc. as the two companies prepare to compete for streaming customers, but it’s not a total war yet.

Disney channels such as ABC, FX, and National Geographic will no longer air Netflix commercials, according to a person familiar with the matter, since the ads would help promote a rival service. But Disney’s ESPN network will still run Netflix spots. And Disney might consider airing a Netflix ad during its Oscars telecast, provided it promotes a movie and not the streaming service itself, said the person, who asked not to be named because the deliberations are private.

The situation reflects the tangled web of the new streaming economy, with onetime partners turning into rivals.

TV networks have long used discretion in running ads from rival media companies. (One exception is movies, which usually get promoted everywhere.) But tensions have grown now that everyone is racing to build a direct relationship with viewers.

Netflix has many other options to advertise its service, through billboards, online marketing, and other TV networks. Netflix was an early adopter of online advertising and still relies more on internet ads than traditional media.

The amount going to Disney was already fairly small. The streaming pioneer only spent about $99 million of its $1.8 billion marketing budget on network TV ads, according to the Wall Street Journal, which cited ad-measurement firm ISpot.TV. The Journal was first to report on Disney barring Netflix ads.

An estimated 13% of that network-TV budget was with Disney-related channels, according to ISpot.TV, but a person familiar with the matter said the actual figure was even smaller.

In the early days of streaming, big media companies saw companies like Netflix and Hulu as critical outlets for reruns of their TV shows and films. That’s now changed as Disney, AT&T Inc.’s WarnerMedia, Comcast Corp. and others launch their own direct-to-consumer video offerings.

Disney started an online service last year called ESPN+, which offers college and some pro sports for $5 a month. The Burbank, California-based company also bought majority control of Hulu with its acquisition of Fox’s entertainment assets earlier this year. Next month, it will introduce Disney+, a $7-a-month service featuring programming from Marvel, Pixar and other family-friendly outlets.

Disney earlier proposed banning ads from all streaming rivals — rather than just Netflix — but it ultimately chose a more targeted approach. It has ongoing relationships with most of the other media giants that are diving into streaming, so there’s more reason to make nice. Amazon.com Inc., which has its own streaming service, remains a key partner with Disney in distributing its channels — through the Fire Stick device and in selling consumer products like Frozen 2 dolls.

“The direct-to-consumer business has evolved, with many more entrants looking to advertise in traditional television, and across our portfolio of networks,” Disney said in a statement. “While the initial decision was strictly advertising based, we reevaluated our strategy to reflect the comprehensive business relationships we have with many of these companies, as direct-to-consumer is one element.” — Bloomberg