Starting Monday, the US government will get another crack at convincing a federal judge to break up Google, after a different judge decided to keep it intact despite finding it to be a monopolist.

Lawyers for Google and the Justice Department will return to a federal courthouse in Alexandria, VA for a roughly two-week trial about how to restore competition to the advertising technology markets that Google illegally monopolized. It comes just weeks after DC District Court Judge Amit Mehta — who issued a historic ruling deeming Google a monopoly in online search — delivered his prescription for restoring competition to the online search market. Mehta’s ruling stopped far short of the government’s major asks to remedy Google’s harm, including denying a requested sale of Google’s Chrome browser, and letting the company keep paying for prime distribution on spots on browsers and phones.

Eastern District of Virginia Judge Leonie Brinkema — who also ruled Google to be a monopolist in two advertising technology markets — is not bound to Mehta’s decision. But she’s undoubtedly paid attention to it. Still, there’s reason for the DOJ to believe it could get a different outcome in the ad tech case when it comes to its request to break up Google.

Unlike in the search case, the part of Google’s business that the government is asking Brinkema to force it to divest was a central product at issue in the trial. The DOJ is asking the judge to require Google to sell its AdX exchange, which facilitates digital transactions for display ads that appear at the top or side of many websites. Brinkema found that Google illegally tied AdX to its publisher ad server, Doubleclick for Publishers (DFP), which is used by websites to sell their ad inventory — so it’s plausible she could find it reasonable to separate one from Google altogether. The government also wants Google to open source the auction logic behind DFP, and if that doesn’t adequately restore competition, it wants the judge to reserve the right to force Google to sell that product, too.

Google, on the other hand, suggests the issues Brinkema found with its dealings can be fixed with a few behavioral tweaks, and characterizes the DOJ’s proposals as an effort to unwind acquisitions that the judge didn’t find to be anticompetitive in and of themselves. Google proposed letting third-party publisher ad servers access real-time bids in AdX — something that the government argued Google only offers to DFP, unfairly disadvantaging rivals and effectively coercing publishers to stick with Google-run platforms. It also says it could allow publishers to export their data without charge, and commit to getting rid of a restriction on how publishers can price their ad inventory known as unified pricing rules. Google could also refrain from using auction tactics like First Look and Last Look in its ad products, which the DOJ had argued unfairly gave Google a leg up.

Like every antitrust trial, there’s still a long road ahead. Google must wait for a remedies ruling before it can appeal the underlying monopoly finding, meaning that even if Brinkema orders a breakup, it could be years until it’s implemented. But how far she’s willing to go will say a lot about the justice system’s willingness to break up Big Tech.