Companies producing and marketing processed high-fat-high-sugar food and drinks face a strategic tension between their core business and the social issue of obesity. For these companies, the social issue of obesity constitutes a strategic social-business tension. We conduct a qualitative study of the print media coverage on the public debate around obesity to analyse how companies discursively respond to strategic tensions around this widely salient issue. We identify the accepting-defensive approach to strategic social-business tensions that companies employ to protect the autonomy over their core business vis-à-vis pressures and demands from the public debate around obesity. We unearth the two discursive mechanisms—choice of discursive tactics and construction of tensions—that underlie this accepting-defensive approach. In contrast to what the literature on organisational tensions suggests, corporate responses to strategic tensions go beyond the dichotomy of accepting-constructive and rejecting-defensive responses. We offer a better understanding of the discursive mechanisms that companies use to maintain autonomy when facing strategic tensions around widely salient social issues.