Contemporary post-truth discourses put the constructivist foundations of Discourse Studies to a test. According to critical observers, discourse analysts have been playing into the hands of Trump, Brexit and right-wing populists by politicising scientific knowledge and undermining the idea of scientific truth. In order to respond to these concerns, this article outlines a Strong Programme in Discourse Studies. While the Strong Programme insists on truths as discursive constructions, in no way does it claim that all ideas have the same truth value or that an idea can become true because somebody wants it to be true. The Strong Programme makes the case for discourse research that is constructivist (it asks how truths are constructed practically) without being relativist (all ideas do not have the same normative quality). Taking inspiration from debates in Science and Technology Studies of the 1970s, the Strong Programme formulates principles for discourse researchers dealing with conflicting truth claims. Discourse analytical explanations of truths of first-order participants and of second-order observers should be symmetrical, heterogeneous, multi-perspectival and reflexive. The Strong Programme discourse research is grounded in the founding traditions of "French" and "Critical" Discourse Studies, which have struggled over questions of truth and reality since the beginning. While critically interrogating the structuralist heritage of these strands, the Strong Programme insists on the practices of making and unmaking ideas through language use no matter whether they appear as true or false to participants and observers. Discourse Studies are encouraged to critically reflect on how hierarchies between knowledges are not only represented but, through their representation, also constituted through discursive practices.