The study of point defects in semiconductors has a long and honorable history. In particular, the detailed understanding of shallow defects in common semiconductors traces back to the classic work of Kohn and Luttinger. However, the study of defects in narrow gap semiconductors represents a much less clear story. Here, both shallow defects (caused by long range potentials) and deep defects (from short range potentials) are far from being completely understood. In this study, all results are calculational and our focus is on the chemical trend of deep levels in narrow gap semiconductors. We study substitutional (including antisite), interstitial and ideal vacancy defects. For substitutional and interstitial impurities, the efects of relaxation are included. For materials like Hg(1-x)Cd(x)Te, we study how the deep levels vary with x, of particular interest is what substitutional and interstitial atoms yield energy levels in the gap i.e. actually produce deep ionized levels. Also, since the main technique utilized is Green's functions, we include some summary of that method.