Many important combinatorial optimization problems can be expressed as constraint satisfaction problems with soft constraints. When problems are too difficult to be solved exactly, approximation methods become the best option. Mini-bucket elimination (MBE) is a well known approximation method for combinatorial optimization problems. It has a control parameter z that allow us to trade time and space for accuracy. In practice it is the space and not the time that limits the execution with high values of z. In this paper we introduce a set of improvements on the way MBE handles memory. The resulting algorithm dfMBE may be orders of magnitude more efficient. As a consequence, higher values of z can be used which, in turn, yields significantly better bounds. We demonstrate our approach in scheduling, probabilistic reasoning and resource allocation problems.