Abstract We propose new mechanisms that can be used by a demand response aggregator to flexibly shift the charging of electric vehicles (EVs) to times where cheap but intermittent renewable energy is in high supply. Here, it is important to consider the constraints and preferences of EV owners, while eliminating the scope for strategic behaviour. To achieve this, we propose, for the first time, a generic class of incentive mechanisms for settings with both varying marginal electricity costs and multidimensional preferences. We show these are dominant strategy incentive compatible, i.e., EV owners are incentivised to report their constraints and preferences truthfully. We also detail a specific instance of this class, show that it achieves ? 98% of the optimal in realistic scenarios and demonstrate how it can be adapted to trade off efficiency with profit.