Some T Tauri stars show a peculiar X-ray spectrum that can be modelled by two components with different absorbing column densities. We seek to explain the soft X-ray component in DG Tau, the best studied of these sources, with an outflow model, taking observations at other wavelengths into consideration. We constrain the outflow properties through spectral fitting and employ simple semi-analytical formulae to describe properties of a shock wave that heats up the X-ray emitting region. The X-ray

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... emission is consistent with its arising from the fastest and innermost component of the optically detected outflow. Only a small fraction of the total mass loss is required for this X-ray emitting component. Our favoured model requires shock velocities between 400 and 500 km/s. For a density >10^5 /cm^3 all dimensions of the shock cooling zone are only a few AU, so even in optical observations this cannot be resolved. This X-ray emission mechanism in outflows may also operate in other, less absorbed T Tauri stars, in addition to corona and accretion spots.