Using National Research Council data, we investigate the determinants of graduation rates in US Ph.D. programmes. We emphasise the impact that support and facilities offered to doctoral students have on completion rates. Significant, strong and positive effects are found for the provision of on-site graduate conferences and dedicated workspace, though there are differences across disciplines in the impact that these have on completion. Other facilities have more limited impact, though results from a quantile regression analysis suggest that some support measures--including student appraisal--may have a stronger positive impact at the bottom end of the distribution.