Obtaining the magnetic properties of non-resolved structures in the solar photosphere is always challenging and problems arise because the inversion is carried out through the numerical minimization of a merit function that depends on the proposed model. We investigate the reliability of inversions in which the stray-light contamination is obtained from the same observations as a local average. In this case, we show that it is fundamental to include the covariance between the observed Stokes profiles and the stray-light contamination. The ensuing modified merit function of the inversion process penalizes large stray-light contaminations simply because of the presence of positive correlations between the observables and the stray-light, fundamentally produced by spatially variable systematics. We caution that using the wrong merit function, artificially large stray-light contaminations might be inferred. Since this effect disappears if the stray-light contamination is obtained as an average over the full field-of-view, we recommend to take into account stray-light contamination using a global approach.Comment: 5 pages, 3 figures, accepted for publication in Ap
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