Theresa May, who has become Britain’s next prime minister by a process of elimination, may nevertheless be the best available choice. Her rivals in the Conservative Party, having persuaded voters to choose to exit the European Union with irresponsible rhetoric and unfulfillable promises, self-destructed one by one. That left May, a veteran cabinet minister and Euroskeptic who nevertheless favored the “remain” side, the last candidate standing.

May, like Britain’s only other female prime minister, Margaret Thatcher, has a reputation for pragmatism and toughness; she will need loads of both.

Foremost among the new government’s problems will be facing the choice between seeking a close association with the EU, including full access to its market, and curbing the outward payments to Brussels and inward flow of EU immigrants, as promised by the Brexit camp. Failure to obtain the former could be devastating to Britain’s service- and finance-heavy economy, but surrender on the latter would enrage many voters.

Prudently, May has indicated she will wait until 2017 to formally trigger the withdrawal process. In the meantime, May is signaling that she will seek to build her own political base with a domestic economic program that abandons her predecessor’s fiscal austerity. May delivered a speech Monday in which she endorsed measures to raise working-class incomes and check executive pay and corporate takeovers.

May, however, also appears to appreciate that the Brexit vote was driven by a backlash against the costs of globalization, including growing inequality. As she put it, the referendum was also “a vote for serious change.” The exit from the EU is not likely to answer those demands. While she negotiates with Brussels, May would be wise to pursue more workable responses.