Despite advances in seasonal climate forecasting using dynamical models, skill in predicting the Indian monsoon by such methods has proven poor. Our analysis identifies a flaw in the hitherto popular design of prediction systems in which atmospheric models are driven with a projected ocean surface temperature. Such a configuration presupposes Indian monsoon variability to be a consequence solely of the atmosphere reacting to the ocean. It is becoming increasingly evident that the Indian monsoon is suitably described as a fully coupled ocean-land-atmospheric system, though implications for skill have not been demonstrated. We discover significant improvements in the skill of Indian monsoon predictions when atmospheric models are not constrained by specified observed SSTs in the Indian Ocean warm pool region. Evidence comes from intercomparing 50-years of monsoon skill in atmospheric models using specified SSTs with skill in coupled ocean atmosphere models.