Elementtattootech of Element Tattoo Supply demonstrates how to properly stretch the skin while giving a tattoo. He notes that he isn't wearing gloves, because he is not actually doing a tattoo in the video. One should always wear gloves when tattooing. If tattooing an arm, grip the other side of the arm (but not too hard, or it might bruise) and it will stretch the skin. Or use the web technique, spreading your fingers over the area. Then the skin will be taut.
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