© 2018 John Wiley & Sons, Ltd. Social psychologists who study racism or prejudice argue that various versions of these are constructed in ways to suppress or minimise their relevance. However, researchers have not particularly examined how knowledge-claims about racism can also be variously made or negotiated in attending to the relevance of racism. We offer such an examination through a discursive psychological analysis of interview talk with Irish nationals on immigration, since in these settings issues of immigration and racism are not readily relevant. Findings show that participants treated how knowledge of racism can be accessed and who has the rights to make knowledge-claims about racism, as relevant. Epistemic access and rights were negotiated in ways that showed sensitivity to possibilities for suppressing alternative claims about racism. These findings are discussed in relation to current social psychological and discursive approaches to racism.