High Resolution Electron Microscopy (HREM) is often used to characterize objects supported by amorphous substrates, usually amorphous carbon. HREM is currently undergoing step change in performance due to aberration correctors. This paper examines the aberration corrected imaging of objects supported by amorphous substrates. In particular, we show that a substantial increase in the ratio of the object contrast to the substrate contrast can be achieved by utilizing the strong variation of phase contrast with height, which is present when the spherical aberration has been adjusted to a small value. This variation is examined using the familiar Weak Phase Object Approximation model from which it is determined that the contrast ratio achieves a maximum at a small nonzero value of the spherical aberration. This result is confirmed by multislice modelling which allows for deviations from the Weak Phase Object Approximation and delocalization effects. One important practical result of this study is the need to place the object of interest on the correct side of the amorphous carbon substrate.