Being Gibraltar is a mighty tough act: Barely 2½ times the area of New York’s Central Park, the Rock has, for much of the past three centuries, faced hostility on its land border with Spain, which ceded it to Britain in 1713. The cession was made in perpetuity—but that has never stopped Spain from treating Gibraltar as a “disputed territory” and trying to wrench it back. The border reopened fully only in 1985, a decade after the death of Gen. Francisco Franco; but even democratic Spain has imposed border closures from time to time as a way to teach Gibraltar who’s boss.

The people of Gibraltar have sided with Britain and against Spain in the sovereignty debate. In a referendum in 1967 on whether sovereignty in the British territory should pass to Spain, 99.64% of citizens voted “no”; and in a 2002 referendum on whether sovereignty in Gibraltar should be shared by the U.K. and Spain, “no” scored 98.97%. Even the most diehard Spanish nationalist wouldn’t spin the smaller second number as progress for Madrid’s cause.

Gibraltar’s latest problems, however, have been of British—not Spanish—making. The European Union was a boon to Gibraltar, as Madrid was required to treat its border as one between two EU member states, as well as to accord to Gibraltar the full range of EU rights. But the Brexit referendum has wrecked this happy situation. In spite of voting to remain in the EU by a very Gibraltarian 96%, the Rock is now bound by the U.K.’s vote to leave. Bowing ominously to Spanish pressure, the EU has stated—in its guidelines for Brexit negotiations—that no new deal with the U.K. would apply to Gibraltar without Spain’s assent.

This veto gives Spain great power to throttle Gibraltar’s economy, and accompanies its latest offer to the U.K. of joint sovereignty over Gibraltar, under which Gibraltarians would keep their political and legal institutions, while having to acknowledge that their territory was as much Spain’s as Britain’s. (Madrid acts as if the Gibraltarians don’t exist. It talks only to London, denying the Rock’s people a voice. The U.K., for its part, has affirmed that it will not accept a change in Gibraltar’s sovereign status without the explicit agreement of Gibraltar’s people.)

To find out how Gibraltar is bracing for life after Brexit, I spoke to Fabian Picardo, its chief minister. (Disclosure: He was my student at Oxford, where I taught him law in 1992.) Mr. Picardo is forthright in his rejection of Spain’s co-sovereignty offer: “People born a particular way can’t be changed because they’re offered a deal. Brits don’t become Germans if they’re offered a good deal, and Gibraltarians don’t become Spaniards because the deal on the table is commercially attractive.”