Targeted policy and governance instruments are essential for developing a carbon dioxide removal (CDR) sector aligned with climate change mitigation scenarios. As a result, a large share of the scientific literature on CDR concentrates on these aspects. However, current CDR deployment and development are mainly driven by private organisations. While their role in CDR governance is generally acknowledged, important context regarding their perspectives, motivations and decision-making processes is lacking. This study addresses this gap by conducting seventy-nine interviews with senior representatives from organisations engaged in the early CDR market, including technology suppliers, credit purchasers, and financiers. We explore their views on key components of fair and equitable CDR systems. Our analysis reveals varying priorities across interviewed actors, including strong regulatory frameworks, market transparency, accountability, funding mechanisms and (climate) justice, emphasising historical responsibility, revenue distribution and community engagement. Additionally, we identify conflicting perspectives on the involvement of oil and gas sectors and the balance between rapid scale-up and thorough, inclusive processes. This research offers critical insights into the role of private organisations in shaping the governance of the emerging CDR sector, highlighting the complex interplay of market dynamics and ethical considerations.