Longtime Google rivals like Yelp and DuckDuckGo received a huge victory on Monday when a federal judge ruled that Google is an illegal monopoly. But their statements on the ruling expressed restraint. That’s because the work of restoring competition has just begun, and the judge has yet to decide what that work will include. With a lot of options on the table, Google’s competitors are pushing for changes they believe will help their businesses, which might be harder than it sounds.

“While we’re heartened by the decision, a strong remedy is critical,” Yelp CEO Jeremy Stoppelman wrote in a blog post after the ruling, referencing the new trial phase that will kick off in September.

“We’ve passed a key milestone, but there’s still a lot of history to be written,” Kamyl Bazbaz, senior vice president of public affairs for DuckDuckGo, said in a statement. “Google will do anything it can to get in the way of progress which is why we hope to see a robust remedies trial that can really dig into all the details, propose an array of remedies that will actually work, and set up a monitoring body to administer them.”

These statements reflect an understanding that Judge Amit Mehta’s decision on how to restore competition will be just as — if not more — important as his finding that Google violated antitrust law. The recently concluded liability phase determined that Google violated the Sherman Act through exclusionary contracts with phone and browser makers to maintain its default search engine position. In the remedies phase, Mehta will decide how to restore competition in general search services and search text advertising. But a weak remedy will simply give Google a pass.

DuckDuckGo knows better than most how important effective remedies are. Google was ruled a monopolist in the European Union years ago, and the region imposed a choice screen in an attempt to create competition, asking device users to select their default search engine. But the approach hasn’t seemingly produced as much of an impact as competitors once hoped — and Google remains overwhelmingly dominant.

“We can’t underscore this enough: the implementation details matter,” Bazbaz said. In the EU, “there are some solutions that are promising, but Google has found it relatively easy to work around their implementations.” DuckDuckGo is calling for a group of “truly independent” technical experts to monitor any remedies imposed by the court, “to ensure Google doesn’t find new ways to give itself preferential treatment.”

DuckDuckGo said that some solutions from Europe could be effective, if implemented in a better way. Instead of showing up only once during initial setup, for instance, a choice screen could pop up “periodically.” Conversely, the company wants a ban on “dark pattern” pop-ups that push people back toward the default, something it says isn’t enforced in the EU.

DuckDuckGo also proposes that the court bar Google from buying default status or preinstallation (which could scuttle its multibillion-dollar deal with Apple) and provide access to its search and ad APIs.

Yelp’s Stoppelman says that Google should be required to “spin off services that have unfairly benefited from its search monopoly, a straightforward and enforceable remedy to prevent future anticompetitive behavior.” The judge should also prohibit Google from using exclusive default search deals and from “self-preferencing its own content in search results,” Stoppelman said.

Other advocates of enforcement against Google, including groups representing publishers that advertise on the service or rely on search for traffic, also have suggestions. On a call with reporters organized by the American Economic Liberties Project (AELP), Digital Content Next CEO Jason Kint said forcing Google to separate its Chrome and Android businesses could be a useful solution. That’s because, Kint says, data from the browser and mobile operating system can be used to expand the scale of search queries and make that product even stronger. “The underlying data that interlocks all that is the critical asset that needs to be constrained,” he says. AELP senior legal counsel Lee Hepner adds that separating the businesses “would open up competition for alternative search rivals on Chrome or Android.”

Whatever happens, the process could be a drawn-out one. Google’s president of global affairs, Kent Walker, has confirmed the company plans to appeal the ruling, saying the decision “recognizes that Google offers the best search engine, but concludes that we shouldn’t be allowed to make it easily available.”

Meanwhile, the specter of artificial intelligence looms over the case, threatening to make moot any proposed solution that doesn’t account for how the whole business model of search could change in the coming years. Hepner said the court could consider solutions like requiring Google to open access to its large language model.

Department of Justice antitrust chief Jonathan Kanter hasn’t commented specifically on what remedies the department will seek, beyond noting they “need to be forward-looking” to account for issues like AI. But he’s previously said that the division would “pursue structural remedies in our conduct cases whenever possible,” meaning breakups, rather than mandates to change certain behaviors. If the DOJ puts forward a broad remedy and Mehta rules in favor of it, the result could be a whole new tech landscape.

“I believe that Judge Mehta’s decision will be as consequential, if not more so, than the Microsoft antitrust case 23 years ago,” wrote Stoppelman. “That decision spurred an era of unprecedented innovation that allowed promising startups to flourish, including Google. It’s exciting to imagine the new technologies and innovation we’ll see emerge as a result of this ruling over the next decade and beyond.”