Current interventions to combat misinformation, including fact-checking, media literacy tips and media coverage of misinformation, may have unintended consequences for democracy. We propose that these interventions may increase scepticism towards all information, including accurate information. Across three online survey experiments in three diverse countries (the United States, Poland and Hong Kong; total n = 6,127), we tested the negative spillover effects of existing strategies and compared them with three alternative interventions against misinformation. We examined how exposure to fact-checking, media literacy tips and media coverage of misinformation affects individuals' perception of both factual and false information, as well as their trust in key democratic institutions. Our results show that while all interventions successfully reduce belief in false information, they also negatively impact the credibility of factual information. This highlights the need for further improved strategies that minimize the harms and maximize the benefits of interventions against misinformation.