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Observations of H2 velocity profiles in the two most clearly defined Orion bullets are extremely difficult to reconcile with existing steady-state shock models. We have observed [Fe II] 1.644‐μm velocity profiles of selected bullets, and H2 1–0 S(1) 2.122‐μm velocity profiles for a series of positions along and across the corresponding bow-shaped shock fronts driven into the surrounding molecular cloud. Integrated [Fe II] velocity profiles of the brightest bullets are consistent with theoretical bow shock predictions. However, observations of broad, singly peaked H2 1–0 S(1) profiles at a range of positions within the most clearly resolved bullet wakes are not consistent with molecular shock modelling. A uniform, collisionally broadened background component which pervades the region in both tracers is inconsistent with fluorescence arising from the ionizing radiation of the Trapezium stars alone.