Experts in children's literature and child development value complexity in the language, socio-emotional content, and structure of books, yet little is known regarding parents' attitudes towards these aspects. The study thus examined how parents' gender, education, and profession, children's age and gender, and frequency of parent-child reading interactions predict parents' support for complexity in children's books. Participants were 104 parents to children aged 4-7. Parents completed questionnaires measuring frequency of shared book reading and levels of support for complexity of children's narrative books in three areas: language, socio-emotional content, and structure. Results showed that parents supported complexity of socio-emotional content, followed by language, and least supported structural complexity. Only parents' profession and frequency of shared book reading interactions predicted support for complexity in books. Parents who read more to their children and parents in social professions showed greater support for complexity. The study stresses the importance of guiding parents to consider a variety of aspects when selecting books to read with their children.