Level an Uneven Subfloor for Vinyl Tile

The following question on leveling a subfloor for vinyl tile was sent in by Roman: I want to put vinyl tiles in my living room and bedroom, and this requires that the floor is smooth and horizontal enough. The subfloor is not too bad, I think. It is largely pretty smooth; however, it is too uneven for me to be able to place a chair or table so that they wouldn’t bounce. I hope there is a cheaper...