Influence diagrams provide a modeling and inference framework for sequential decision problems, representing the probabilistic knowledge by a Bayesian network and the preferences of an agent by utility functions over the random variables and decision variables. The time and space complexity of computing the maximum expected utility (MEU) and its maximizing policy is exponential in the induced width of the underlying graphical model, which is often prohibitively large due to the growth of the requisite information for making a sequence of decisions. In this paper, we develop a weighted mini-bucket approach for bounding the MEU. These bounds can be used as a stand-alone approximation that can be improved as a function of a controlling i-bound parameter, or as a heuristic function to guide subsequent search. We evaluate the scheme empirically against the current state of the art, illustrating its potential.