Chemical vapor deposition synthesis of graphene on copper foil from methane is the most promising technology for industrial production. However, an important problem of the formation of the second and subsequent graphene layers during synthesis arises due to the strong roughness of the initial copper foil. Here we demonstrate the various approaches to prepare a smooth copper surface before graphene synthesis to reduce the formation of multi-layer graphene islands. Six methods of surface processing of copper foils are studied, and the decrease of the roughness from 250 to as low as 80 nm is achieved. The correlation between roughness and the formation of multi-layer graphene is demonstrated. Under optimized conditions of surface treatment, the content of the multi-layer graphene islands drops from 9 to 2.1%. The quality and the number of layers of synthesized graphene are analyzed by Raman spectroscopy, scanning electron microscopy, and measurements of charge mobility.