Since busses take up signi_cant fraction of chip-area, the bus capacitances are often considerable, and the bus power may account for as much as 40% of the total power consumed on the chip [5]. In applications where the integrity of data is not very important, data may be changed by 3 to 5% without losing too much information. One such application is that of a binary-encoded image, in which case the human eye cannot perceive the small change. However, these small changes can signi_cantly reduce the number of transitions on the data bus and thus the power/energy consumed. We address the following problem: Given a sequence of n k-bit data words and an error-tolerance e% (i.e., at most e% of the data bits are permitted to change), select the bits to be modified so that the total number of transitions is minimized. We show that a greedy strategy is not always optimum. We propose a linear-time dynamic programming based algorithm that generates an optimum solution to this problem. The experimental results for randomly generated data with a uniform distribution indicate that by changing e% data bits, the transitions can be reduced, on average, by 4e%.