Automotive Safety Integrity Levels (ASILs) are used by ISO 26262, the new automotive functional safety standard, to categorize the stringency of safety requirements. In the course of a hierarchical system design, ASILs are it-eratively allocated to subsystems and components. This ASIL decomposition allows for redundant elements to share the responsibility of meeting a given ASIL and finding efficient decomposition solutions has a significant, positive, impact on development costs. This paper describes a novel technique that uses Tabu Search to explore the solution space efficiently. We have applied the technique to a case study of a hybrid braking system.