In additive manufacturing (AM) technologies, support structures are used to anchor a part to the base plate and to prevent the part from distortions and dimensional deviations due to high thermal gradients during manufacturing. Because the support structures do not contribute any value to the part and need to be removed after manufacturing with extra costs and time, different studies have focused on minimizing the use of such structures. However, it is almost impossible to totally eliminate the need for support structures, especially in very complex parts with different overhang surfaces. Therefore, it is very important to optimize the support structure geometry to reduce support volume and consequently costs and time. Thus, the aim of this study is to investigate the effect of tooth support geometrical parameters, namely tooth height, top length, base length, and base interval on the part's dimensional accuracy, surface roughness, microhardness through thickness, and support volume used in overhangs produced by laser powder bed fusion AM technology from Inconel 718 material. The L9 Taguchi design method was used to reduce the number of experiments. The efficiency of the parameters was determined by analysis of variance. Analyses of signal-to-noise ratios were used to obtain the optimum support parameter combination. The study reveals that tooth height has the highest effect on support volume and dimensional accuracy. Tooth base length was found to be the most effective parameter on surface roughness and microhardness through thickness.