We call on research funding organisations to experiment with different models for integrating partial randomisation into their grant allocation processes as well as to assess the feasibility, the potential implications, and the perceptions of such models. Traditional models of grant allocation have usually been based on peer review to rank applications and allocate grants. These models have been shown to suffer from various shortcomings. In particular, we believe that partial randomisation holds the potential of being more fair, more efficient, and more diverse. In addition, it may lead to more responsible research practices. We outline a proposal for such a grant allocation process and sketch various arguments in favour of it. We also address potential counterarguments and conclude that partial randomisation in grant allocation holds the potential to lead to many benefits and therefore warrants further experimentation and implementation.