Traceability management relies on a supporting model, the traceability information model (TIM), that defines which types of relationships exist between which artifacts and contains additional constraints such as multiplicities. Constructing a TIM that is fit for purpose is crucial to ensure that a traceability strategy yields the desired benefits. However, which design decisions are critical in the construction of TIMs and which impact they have on the usefulness and applicability of traceability is still an open question. In this paper, we use two cases of TIMs constructed for safety-critical, automotive systems with industrial safety experts, to identify key design decisions. We also propose a comparison scheme for TIMs based on a systematic literature review and evaluate the two cases as well as TIMs from the literature according to the scheme. Based on our analyses, we thus derive key insights into TIM construction and the design decisions that ensure that a TIM is fit for purpose.