“COCKROACHESQUE” is an unusual compliment, unless you are a Liberal Democrat. Tim Farron, a Lib Dem MP and former leader, uses the term to describe his party’s performance in local elections on May 3rd, when it again showed its knack for survival in hostile conditions. Since near-wipeout in the general election of 2015, when they lost 86% of their MPs and 66% of their voters, the Lib Dems have battled to stay alive. Yet they emerged from this month’s local polls as the only party justified in calling the night a success.

They gained four councils: Kingston, Richmond, South Cambridgeshire and Three Rivers, in Hertfordshire. They even came within a few hundred votes of snatching Hull, demonstrating that the Lib Dems have some appeal outside Remain-voting enclaves in the south. One analysis estimated that the party would have taken 14% of the vote if the elections had taken place nationwide.

The party’s strategy looks faintly contradictory. On the one hand, the Lib Dems are trying to position themselves as the natural home for the “none of the above” voter. Mr Farron hopes to find more supporters like the man who said he would back the Lib Dems because “Tories are evil, Labour can’t add up and you are all right”. “People spend millions on branding that is less succinct than that,” Mr Farron says.

On the other hand, the party is cheerfully divisive on the subject of Brexit, which it is dead against and would like to reverse via a referendum on the final deal. This approach gives the Lib Dems the advantages of sincerity, unity and clarity, none of which can be said of Labour or the Conservatives when it comes to the EU. But becoming a one-issue party—a sort of UK Independence Party for Remainers—has risks, not least alienating the 17m people who voted for Brexit. Bold policies in other areas, such as raising income tax to fund the National Health Service, give the party something else to talk about.

It will be the Lib Dems’ ability to win over wavering Tory voters that will decide whether the party has a viable future. The Lib Dems finished second in 38 constituencies at last year’s general election. In 29 of these, it was the Conservatives who beat them. But translating local success into a national breakthrough is not easy, as the Lib Dems have long known. Two-party politics has returned. The wide ideological gulf that has opened up between Labour and the Conservatives may make a vote for the Lib Dems seem risky at the next general election, due in 2022.

This leaves the Lib Dems with a Douglas Adams dilemma. In “The Hitchhiker’s Guide to the Galaxy”, Mr Adams described a planet on which lizards ruled over people, even though it was a democracy. People repeatedly voted for lizards because otherwise “the wrong lizard might get in.” The Lib Dems offer another way: forget the lizards, vote for the cockroaches instead.