The current evolution of the ATM system, led by the SESAR programme in Europe and the NextGen programme in the US, is foreseen to bring a paradigm shift to the work of the air traffic controller. Rather than the current primarily tactical control method, one aims for the introduction of more strategic, 4D (space and time) trajectory management. In both programmes a central role is foreseen for the human operator, aided by higher levels of automation and advanced decision-support tools. Previous work has shown promising results in the design of such automated support tools, however, issues with controller acceptance and intuitiveness were found to be key for their overall acceptability. This paper presents a concept decision-support tool for 4D trajectory management that aims to overcome these issues by directly visualizing action-relevant solution spaces. Rather than imposing a certain control strategy, the solution space visualizes all possible control actions, regardless of their optimality. Results of preliminary validation experiments with partial implementations of the solution space representation demonstrated the viability of the concept, but also highlighted areas for improvement.