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We implement a linear model for mitigating the effect of observing conditions and other sources of contamination in galaxy clustering analyses. Our treatment improves upon the fiducial systematics treatment of the Dark Energy Survey (DES) Year 1 (Y1) cosmology analysis in four crucial ways. Specifically, our treatment: 1) does not require decisions as to which observable systematics are significant and which are not, allowing for the possibility of multiple maps adding coherently to give rise to significant bias even if no single map leads to a significant bias by itself; 2) characterizes both the statistical and systematic uncertainty in our mitigation procedure, allowing us to propagate said uncertainties into the reported cosmological constraints; 3) explicitly exploits the full spatial structure of the galaxy density field to differentiate between cosmology-sourced and systematics-sourced fluctuations within the galaxy density field; 4) is fully automated, and can therefore be trivially applied to any data set. The updated correlation function for the DES Y1 redMaGiC catalog minimally impacts the cosmological posteriors from that analysis. Encouragingly, our analysis does improve the goodness of fit statistic of the DES Y1 3$\times$2pt data set ($Δχ^2 = -6.5$ with no additional parameters). This improvement is due in nearly equal parts to both the change in the correlation function and the added statistical and systematic uncertainties associated with our method. We expect the difference in mitigation techniques to become more important in future work as the size of cosmological data sets grows.