To win a policy debate, political actors may apply two analytically distinct counterframing strategies, rhetoric and heresthetic. Rhetoric is when counterarguments are formulated in the original dimension of the debate, while heresthetic is using arguments in a different dimension compared to the original frame. Although both rhetoric and heresthetic are ubiquitous phenomena in the process of public opinion formation, there are no general rules to specify their efficacy. Drawing on a survey experiment carried out in Hungary in 2020 (N = 2000), this paper uncovers the factors determining the effect of the two strategies. Introducing a conceptual distinction between open and trade-off framing situations, the paper demonstrates that the structure of the situation matters. While heresthetic has a robust effect in trade-off framing situations, rhetoric may have a strong impact in open framing situations. Moreover, the effectiveness of counterframing depends on the party affiliation of respondents and the strength of their related attitudes.