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If you are using a pencil liner, consider putting your eyeliner in the fridge for 10 or so minutes if you notice it is soft. Eyeliner is made mostly of wax, and when wax is warm it melts and smudges. If you live in a warm climate or your eyeliner is above room temperature, stick it in the fridge. Apply one even layer of eyeliner to your eyelid right at your lash line. Apply more eyeliner if needed. Several thin layers of eyeliner will stay in place better than thick layers. Do not apply too much liner, because having excess liner can cause fallout and smudging. When you apply your eyeliner, use a light hand. Your eye area is very delicate and being rough on it will cause your eyes to water. Watering eyes causes makeup to shift, so be gentle when applying your liner. If you want to do everything you can to avoid smudging, avoid putting eyeliner on your waterline. Your waterline is the rim of your eyelid that is against the eye, between the base of your lashes and your eyeball. Your waterline is very sensitive, and applying eyeliner there can cause your eyes to water. Watering eyes and tearing causes your eyeliner to shift downward, giving you the smudged, raccoon look.  Some prefer the look of liner on their waterline rather than on their lash line. If you are not willing to give up putting eyeliner on your waterline, make sure that you are using a liner that is not irritating to your eyes. This may mean investing in a more expensive product than most drugstore eyeliners.
Use cooled eyeliner. Apply your eyeliner. Use a light hand. Avoid your waterline.