Apple wants one more shot at clearing its name of e-book antitrust violations.

Having lost a federal court appeal earlier this year, Apple will ask the U.S. Supreme Court to overturn a ruling that the company conspired with publishers to fix e-book prices, Fortune reports.

Apple lost its original case in 2013, after being sued by the U.S. Department of Justice along with 33 states and U.S. territories. At the time, U.S. District Court Judge Denise Cote found that Apple broke the law when it convinced five major publishers to adopt the same “agency” pricing model, in which they set their own prices and agreed not to offer lower prices elsewhere. This had the effect of raising some prices at rival e-book seller Amazon, as publishers abandoned the “wholesale” model that let Amazon set e-book rates on its own.

In the past, Apple has argued that it was making the market more competitive by weakening Amazon’s grip. The company reiterated that rationale in a note to the Supreme Court, saying “disruptive entry into new or stagnant markets” requires the type of conduct Apple engaged in. (The actual legal argument seems fairly technical, making the case that Apple didn’t engage in “horizontal” price fixing, and therefore must be judged on the competitive effects of its behavior.)

Apple hasn’t technically submitted its formal request with the High Court yet, but has asked for a 30-day extension to do so. As Fortune points out, the extension request outlines much of Apple’s argument for seeking the Supreme Court’s review. Of course, the court can still deny Apple’s request to have its case heard at all.

Why this matters: The monetary stakes in this case are fairly low for a huge company like Apple, with the company agreeing to pay out $450 million if it exhausts all its appeal options. But Apple has said previously that the case is “about principles and values,” and it’s possible that the ruling is having deeper ramifications. As reported earlier this year, Apple may have tried convincing record labels to kill the free version of Spotify to help pave the way for Apple Music. While Spotify’s free version still exists, Apple is now facing new antitrust inquiries from several state attorneys general.