Many islands have high electricity prices due to the reliance on imported diesel. However, hybrid energy systems (HES) which combine renewable generation with backup generators and energy storage are becoming cost competitive. Diesel usually provides about 10% of the demand because most renewables are non-dispatchable and thus the complete decarbonisation requires massively oversized renewable generation and storage. By including renewables with different resource profiles and demand side management (DSM), the diesel consumption could be decreased without increasing storage and renewable generation capacities. Here a framework for the design and optimisation of HES using wind, wave and solar generation and DSM is introduced. For the Mediterranean it is shown that wave energy is not competitive but that DSM reduces the emissions and costs by 21 and 8%. In the North Sea, DSM has lower benefits because waves act as an energy store for the wind. Thus, the combination of wave energy converters (WECs) and wind turbines significantly reduces the need for backup generation and energy storage which leads to large reductions in costs (up to 40%) and emissions (up to 60%). DSM and WECs can both simultaneously reduce the cost and emissions of HES but need to be designed for the particular circumstances.