Motivated by earlier research highlighting Swedish teachers' beliefs that the setting of homework compromises deep-seated principles of educational equity, this paper presents an exploratory study of Swedish parents' perspectives on homework in their year-one children's learning. Twenty-five parents, drawn from three demographically different schools in the Stockholm region, participated in semi-structured interviews. The interviews, broadly focused on how parents support their children's learning and including questions about homework in general and mathematics homework in particular, were transcribed and data subjected to a constant comparison analytical process. This yielded four broad themes, highlighting considerable variation in how parents perceive the relationship between homework and educational equity. First, all parents spoke appreciatively of their children receiving reading homework and, in so doing, indicated a collective construal that reading homework is neither homework nor a threat to equity. Second, four parents, despite their enthusiasm for reading homework, opposed the setting of any homework due to its potential compromise of family life. Third, seven parents indicated that they would appreciate mathematics homework where it were not a threat to equity. Finally, fourteen parents, despite acknowledging homework's potential compromise to equity, were unequivocally in favour of mathematics homework being set to their children.