Rising demand from electrical heating and vehicles will drive major distribution network reinforcement costs unless 24-hour demand profiles can be levelled. We propose a demand response scheme in which the electricity supplier provides a signal to a “smart home” control unit that manages the consumer’s appliances using a novel approach for reconciliation of the consumer’s needs and desires with the incentives supplied by the signal. The control unit allocates demand randomly in timeslots that are acceptable to the consumer but with a probability biased in accordance with the signal provided by the supplier. This behaviour ensures that demand response is predictable and stable and allows demand to be shaped in a way that can satisfy distribution network constraints.