In this paper, we present a directly applicable scheme for electricity consumption shifting and effective demand curve flattening. The scheme can employ the services of either individual or cooperating consumer agents alike. Agents participating in the scheme, however, are motivated to form cooperatives, in order to reduce their electricity bills via lower group prices granted for sizable consumption shifting from high to low demand time intervals. The scheme takes into account individual costs, and uses a strictly proper scoring rule to reward contributors according to efficiency. Cooperative members, in particular, can attain variable reduced electricity price rates, given their different load shifting capabilities. This allows even agents with initially forbidding shifting costs to participate in the scheme, and is achieved by a weakly budget-balanced, truthful reward sharing mechanism. We provide four variants of this approach, and evaluate it experimentally.