In many countries, right-wing populist parties have gained electoral support by attracting voters from mainstream left parties. This has prompted public and scholarly debate about whether mainstream left parties can regain political power by taking a more restrictive position on immigration, a so-called accommodation strategy. However, selection bias confounds observational estimates of the effectiveness of this strategy. This letter reports the results of a survey experiment conducted among Danish voters during a unique political situation in which the mainstream left party's position on immigration is ambiguous, enabling experimental manipulation of voters' perceptions of the party's position. The authors show that, consistent with spatial models of politics, accommodation attracts anti-immigration voters and repels pro-immigration voters. Because repelled voters defect to other left parties, while attracted voters come from right parties, accommodation increases overall support for parties that support a mainstream left government. The results demonstrate that in some contexts, accommodation can improve the political prospects of the mainstream left.