Owing to its high conductivity, graphene holds promise as an electrode for energy devices such as batteries and photovoltaics. However, to this end, the work function and doping levels in graphene need to be precisely tuned. One promising route for modifying graphene's electronic properties is via controlled covalent electrochemical grafting of molecules. We show that by employing diaryliodonium salts instead of the commonly used diazonium salts, spontaneous functionalization is avoided. This allows for precise tuning of the grafting density. By employing bis(4-nitrophenyl)iodonium(III) tetrafluoroborate (DNP) salt calibration curves, the surface functionalization density (coverage) of glassy carbon was controlled using cyclic voltammetry in varying salt concentrations. These electro-grafting conditions and calibration curves translated directly over to modifying single layer epitaxial graphene substrates (grown on insulating 6H-SiC (0001)). In addition to quantifying the functionalization densities using electrochemical methods, samples with low grafting densities were characterized by low-temperature scanning tunneling microscopy (LT-STM). We show that the use of buffer-layer free graphene substrates is required for clear observation of the nitrophenyl modifications. Atomically-resolved STM images of single site modifications were obtained, showing no preferential grafting at defect sites or SiC step edges as supposed previously in the literature. Most of the grafts exhibit threefold symmetry, but occasional extended modifications (larger than 4 nm) were observed as well. (C) 2015 Elsevier B.V. All rights reserved.