We describe a system, TraumAID, which has been designed to provide decision support throughout the initial definitive management of severely injured patients (i.e., after their initial evaluation, resuscitation, and stabilization). Over the course of initial definitive management, TraumAID recommends appropriate procedures to be carried out, based on currently available evidence and on the complexity and urgency of the situation. TraumAID's ability to deal flexibly with complex and often urgent situations comes from its ability to reason separately about the management goals that should be achieved and about the means that are situationally appropriate for achieving them. In this paper, we describe TraumAID's approach to trauma management in more detail, showing in particular how it enables TraumAID to adapt its reasoning and recommendations to the urgency with which a patient's condition must be addressed.