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To remove layers from the surface of something in order to make it level or smooth. A noun or pronoun can be used between "level" and "down." The timber was a bit uneven where they had cut it with the hand saw, so I leveled it down with my power sander. They brought in a steam roller to level down the ground around the construction site before laying down the topsoil.
level something down
to make something level or smooth. The soil is very uneven in this part of the garden. Would you please level it down? The huge earth-moving machines leveled the hill down in preparation for the building of the highway.