A challenge in molecular electronics is to control the strength of the molecule–electrode coupling to optimize device performance. Here we show that non-covalent contacts between the active molecular component (in this case, ferrocenyl of a ferrocenyl–alkanethiol self-assembled monolayer (SAM)) and the electrodes allow for robust coupling with minimal energy broadening of the molecular level, precisely what is required to maximize the rectification ratio of a molecular diode. In contrast, strong chemisorbed contacts through the ferrocenyl result in large energy broadening, leakage currents and poor device performance. By gradually shifting the ferrocenyl from the top to the bottom of the SAM, we map the shape of the electrostatic potential profile across the molecules and we are able to control the direction of rectification by tuning the ferrocenyl–electrode coupling parameters. Our demonstrated control of the molecule–electrode coupling is important for rational design of materials that rely on charge transport across organic–inorganic interfaces.