Using a model of oscillating dipoles, we simulate the intensity of the G-band in the Raman signal from structures consisting of graphene, separated by an arbitrary buffer layer from a substrate. It is found that a structure with an optimized buffer layer refractive index and thickness exhibits a Raman signal which is nearly 50 times more intense than that from the same structure with a non-optimized buffer layer. The theoretical simulations are verified by Raman measurements on structures consisting of a layer of graphene on SiO2 and Al2O3 buffer layers. The optical contrast of the single graphene layer is calculated for an arbitrary buffer layer. It was found that both the Raman intensity and optical contrast can be maximized by varying the buffer layer thickness. Copyright © 2013 John Wiley & Sons, Ltd.