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The European Union is pushing to exempt its wine and spirit exports to the U.S. from tariffs, an EU official said, as both sides work toward fine-tuning a deal.

Wines, spirits and beer are all important products for the EU, the official said on Tuesday.

French politicians have called for alcoholic beverages to be exempt from a baseline 15% tariff that will hit a majority of goods from the EU later this week as part of the trade deal.

The EU official said negotiators hope to have more news soon on which products would be included in a list of goods that will be exempted from that rate. He said there are a range of products—including medical devices and chemicals—that European policymakers believe should have an effective zero-tariff placed on them as part of the agreement.

“We fight for every product and every industry,” they said, adding that EU negotiators are trying to get as many products as possible included in the list of exemptions. “We hope to see more clarity and more focus as we progress,” they said.

Another EU official said the bloc expects that cork and cork-related products could be on the list of exemptions in the future. “There are a certain number of natural resources which the U.S. also has indicated an interest in being able to continue importing at zero duties and cork is among those,” they said.

Officials also highlighted that the 15% baseline is an “all-inclusive” tariff rate, which means it won’t be stacked on top of existing tariffs.

The U.S. is still investigating some sectors—including pharmaceuticals and semiconductors—to assess whether to impose tariffs on them. If it eventually does, the EU officials said they expect exports from the EU in those areas will be capped at 15%. Talks on steel and aluminum duties are taking longer while details on export quotas are hashed out, one official said.

The EU and U.S. are in the final stages of drafting a joint statement on their trade deal, which would essentially be a nonbinding rundown of what both sides have agreed to.

That should include a range of political agreements touching not only on tariffs but also on EU regulations that U.S. President Trump has criticized as making it harder for businesses to operate in the bloc, officials said.

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“We do not change our rules. In some areas however, we are ready to discuss streamlining ways to complying with rules,” one official said, adding that any work to simplify compliance wouldn’t discriminate in favor of American companies.

The European Commission is already in the process of simplifying a raft of legal texts governing things like corporate sustainability reporting and data protection in a broader push to inject life into the European economy.

One of the officials also said the EU won’t cede ground on enforcing the Digital Markets Act, a rulebook designed to rein in the market power of U.S. tech giants like Apple that has drawn ire from the Trump administration in recent months.

Write to Edith Hancock at edith.hancock@wsj.com