An important computational goal of the visual system is “representational untangling” (RU): representing increasingly complex features of visual scenes in an easily decodable format. RU is typically assumed to be achieved in high-level visual cortices via several stages of cortical processing. Here we show, using a canonical population coding model, that RU of low-level orientation information is already performed at the first cortical stage of visual processing, but not before that, by a fundamental cellular-level property: the thresholded firing rate nonlinearity of simple cells in the primary visual cortex (V1). We identified specific, experimentally measurable parameters that determined the optimal firing threshold for RU and found that the thresholds of V1 simple cells extracted from in vivo recordings in awake behaving mice were near optimal. These results suggest that information re-formatting, rather than maximisation, may already be a relevant computational goal for the early visual system.