Genetic services for individuals affected by cleft lip and/or palate (CL/P) and their families are an important aspect of clinical care; yet debate exists as to how this service should be offered. This study explored the utility, acceptability, and delivery of genetic services from the perspectives of cleft-specialist clinicians, genetic counsellors, and affected families. Analysis of data collected from three focus groups and eleven individual interviews identified two overarching themes: “Referring patients and families to genetic services”, and “The role of a genetic specialist in the context of CL/P”. The first examines common reasons for referral to the genetics service, how best to judge the timing of a referral, and the optimal approach to the delivery of sensitive genetic information. The second theme discusses the role of the genetic specialist in the context of cleft care, including the optimal management of affected individuals and their families, and the delivery of basic genetics training and support for health professionals working in other disciplines. A model for the effective delivery of genetic services in CL/P is subsequently proposed. Coordination and financial implications of the proposed model ultimately require further consideration and evaluation to determine its effectiveness.