This article focuses on the impact of attitude strength on the acceptance of a green service, the acceptance of green family insurances. Two dimensions of attitude strength are distinguished: embeddedness and commitment. Cognitive elaboration, information seeking and selective judgement are introduced as mediators. It is shown that embeddedness has a positive impact on cognitive elaboration whereas commitment has a positive effect on information seeking. Furthermore, cognitive elaboration has a positive impact on information seeking and both cognitive elaboration and information seeking have a positive effect on the selective judgement. This selective judgement clearly positively influences domain specific intended behavior or the acceptance of the green family insurance.