Computer Graphics has a long history in the design of effective algorithms for handling contact and friction between solid objects. For the sake of simplicity, most methods rely on low-order primitives such as line segments or triangles, both for the detection and the response stages. In this paper we carefully analyse, in the case of fibre systems, the impact of such choices on the retrieved contact forces. We highlight the presence of force artifacts due to the low-order geometry used for contact detection, that appear all the more visible as the fibre geometry at contact is curved. To remove such artifacts we develop an accurate detection scheme between two smooth curves, relying on an efficient adaptive pruning strategy. We use this algorithm to detect contact between super-helices at high precision, allowing us to recover, in the range of wavy to highly curly fibres, much smoother force profiles than with a classical segment-based strategy. Furthermore, our approach offers better scaling properties in terms of efficiency vs. precision compared to segment-based approaches, making it attractive for applications where accurate and reliable forces are desired. Finally, we demonstrate the robustness and accuracy of our fully high-order approach on a challenging hair combing scenario.