There is growing concern that collision risk in low Earth orbit is inadequately managed, necessitating new strategies. Based on discussions held at a multistakeholder workshop organized by EPFL in May 2021, this paper presents some challenges, or governance deficits, in the assessment and management of collision risk, and offers some paths for improvements in both domains. Addressing the governance deficits will require enhanced collaboration between states and between public and private actors. While there is a need to improve risk assessment and conduct thorough cost-benefit analyses of management strategies, achieving a complete picture is elusive, given the complexity of the problem and the range of response strategies available. However, the lack of a complete picture should not be a reason to postpone action, as sufficient information to make decisions regarding some management policies is available. Adopting a multidimensional approach and focusing on measures that have the potential for rapid improvements would help secure stakeholder buy-in and lay the groundwork for pursuing strategies that will likely be the most cost-effective in the longer term.