Prevalence studies indicate that higher degree research (Master's and Doctoral) students experience high rates of psychological distress. As a result, universities are seeking evidence-based interventions to better support the mental wellbeing of this student cohort. The present study contributes to that evidence base by asking higher degree research students (HDRs) from a large Australian research-intensive university what they think should be done to improve their wellbeing. After inductively analysing 595 open-ended survey responses, nine themes emerged. The four most prominent themes were culture and community, support services, supervisors and supervision practices, and peer engagement and networking. These themes are interpreted by drawing on the Job Demands-Resources theory of occupational stress. We also compare our findings with typologies of 'doctoral challenges' developed in prior research to extend and refine the 'roadmap' for policy, action and research to better understand and address the high levels of psychological distress that HDRs experience. Overall, the findings of this study suggest that HDRs are likely to benefit from a whole-of-university approach to supporting their wellbeing, and from an academic research culture that values the wellbeing of all its members.