Here is one of the toughest questions British Prime Minister Theresa May will have to answer as she maps out her thinking on the exit negotiations from the European Union, starting with a speech on Tuesday: Should the U.K. seek to stay, at least temporarily, in the EU’s customs union?

At stake are critical issues such as how quickly Britain could tie up new trade deals, whether Brexit will herald tariffs on U.K.-EU trade and how free the U.K. will be to shift away from EU product regulation.

A customs union eliminates or reduces internal customs barriers to trade and imposes a common external tariff on imports from nonmember countries. While some pieces of the Brexit puzzle are starting to become clearer, the government’s view on the customs union remains murky.

Mrs. May’s speech to her Conservative Party conference in October would seem to make British membership of the customs union difficult. In it, she insisted that Britain would regain control of its own laws and wouldn’t “return to the jurisdiction of the European Court of Justice.”

But that doesn’t quite block off the path. For starters, the U.K. is likely to seek a transitional accord for a few years with the EU, smoothing the ride to a final post-Brexit relationship, and a customs union could be part of that. Britain and the EU could also agree a joint dispute-settlement panel outside of the ECJ.

Opponents of customs-union membership argue that it prevents Britain from signing its own trade deals with other countries, a key objective of free-trade Brexiteers such as International Trade Secretary Liam Fox. Inside the customs union, Britain would remain bound by the EU’s external tariff but, once outside the EU, with no say in setting the bloc’s trade policy or tariffs.

The U.K. would also need to put a brake on overhauling its rules and regulations. Diverging too far from EU rules to undercut European environmental or health standards, for example, would quickly fall foul of any dispute panel, which in any case would need to heavily factor in ECJ decisions.

On the other hand, there are important economic advantages of remaining in the customs union. Number one, there would be no imposition of tariffs on trade between the U.K. and EU. Britain would also continue to enjoy the benefits of the EU’s dozens of trade deals from Canada to South Korea.

U.K. products wouldn’t have to submit to customs checks, a cumbersome process that could cost British business many billions of pounds in administration costs and port delays. And there is no legal reason, although EU members may object, why customs-union membership would prevent the U.K. from claiming the right to limit immigration from the EU, a key British objective.

Yet, Mrs. May has said a decision on the customs union may not be a “binary choice.” U.K. officials and lawmakers are exploring the options.

Turkey is one example. The country isn’t a customs-union member but it has a customs agreement with the EU that eliminates tariffs on most industrial goods but not on services and agriculture.

Turkish goods must still submit to customs checks and, while Turkey can sign trade deals with other countries, it is constrained by having to adhere to the EU’s common external tariff. Moreover, when the EU signs a free-trade accord with another country, Turkey is obliged to open its market to that country but the other country doesn’t have to reciprocate.

The Turkish model isn’t a perfect template either for a service-heavy economy such as Britain’s. However, there is nothing stopping the U.K. seeking a differently shaped customs deal with the EU.

Vicky Ford, a British lawmaker in the European Parliament, says the U.K. could also leave the customs union but find ways to mitigate the costs. One is to lighten as much as possible the regulations and procedures around customs checks the EU imposes on U.K. exporters.

Norway, for example, has a relatively light-touch arrangement with the EU. There are random custom checks to ensure rules are being followed but products are not checked individually. The onus is on Norwegian exporters to ensure and declare that the goods they’re sending to the EU can enter tariff-free.

The second is the future arrangements around so-called country-of-origin rules. Assuming that Britain seeks a free-trade deal with the EU, the rules around what counts as a British product and what doesn’t will be crucial for advanced British manufacturers with their international supply chains.

If the U.K. can ensure that products such as cars will count as British exports and enjoy tariff-free status, even if they have a significant share of their value-added coming from outside Britain or the EU, it would be a major bonus.

Such favorable agreements are possible. The stumbling block will likely be the abiding fear among EU leaders that a cherry-picked deal for the U.K. would create incentives for other countries to follow suit.