Background  Pregnancy and the first years of life are important times for future child well‐being. Early identification of families and children who might be likely to experience poorer outcomes could enable health professionals and parents to work together to promote each child’s well‐being. Little is known about the acceptability and feasibility of such an approach to parents.Objective  To investigate parents’ views about how health professionals should identify and work with families who may benefit from additional input to maximize their children’s future health and well‐being.Design  A qualitative study using focus groups.Setting and participants  Eleven focus groups were conducted with a total of 54 parents; 42 mothers and 12 fathers living in the north of England.Results  Parents welcomed the idea of preventive services. They strongly believed that everyone should have access to services to enhance child well‐being whilst recognizing that some families need additional support. Making judgements about who should receive additional services based on specific criteria evoked powerful emotions because of the implication of failure. Parents projected a belief in themselves as ‘good parents’ even in adverse circumstances.Conclusions  Targeted additional preventive services can be acceptable and welcome if health professionals introduce them sensitively, in the context of an existing relationship, providing parents are active participants.