Behaviour problems and poor literacy levels are each independently associated with a lower quality of life in childhood, and carry forward to predict much poorer outcomes in adulthood. Longitudinal surveys show that the dimensions of parenting that influence child behaviour and child literacy differ. The aspects of parenting that promote good behaviour concern the quality of the relationship, for example giving warmth and encouragement while calmly enforcing clear limits. In contrast, the aspects that promote literacy are regular reading with the child in a manner that is sensitive to their ability level. To help children with difficulties, there are many evidence-based parenting programmes to improve parent-child relationship quality, but very few address literacy. This paper reviews evidence on these issues, illustrated by our own previous preventive trials that combined a parenting programme addressing relationships (Incredible Years; IY) with a new parenting programme addressing literacy (Supporting Parents on Kids Education; SPOKES). Because this combination improved both child behaviour and literacy, a new randomized controlled trial called Helping Children Achieve is underway to disentangle the mode of action of each component by comparing the effects of: (1) a relationship programme alone (IY); with (2) a literacy programme alone (SPOKES); (3) both combined; and (4) an information helpline (control group). The results are not yet known but should answer whether programmes that target relationships also improve child literacy, and whether programmes that target literacy also improve behaviour. The findings will inform strategies to reduce social inequality and help young children achieve their potential.