This paper presents and evaluates a novel approach to decrease the power consumption of epidemic information dissemination in sensor networks. In essence, our strategy consists in modulating the transmission range of sensors before they send messages. Since the range modulation follows a power-law probability distribution, we qualify our approach to information dissemination as being a power-law. An obvious consequence of this strategy is that many nodes can reach few neighbors, while few nodes can reach many neighbors. To evaluate the effects of our approach, we inject the power-law range modulation into four existing epidemic algorithms and we compare their performances with their original versions, based on a fixed transmission range or on a uniform distribution of transmission ranges. This evaluation shows that our power-law approach improves the efficiency of the original algorithms in terms of power consumption, with no negative impact of their effectiveness, measured in terms of how many nodes have been reached after the dissemination.