Problems in domains that are highly dimensional, inhomogeneous, and context dependent are difficult to support by computational tools. If solutions to these problems must be devised based on little information that is highly subjective, the situation worsens. In this paper, we propose a new case-based reasoning (CBR) method for addressing such problems. The method is based on augmenting case descriptions with knowledge in the form of influence graphs. We use these influence graphs to cluster the space of problems. These clusters, in turn, are used to retrieve the most relevant cases given a new problem specified only by three to four attributes. We tested the system in a lab setting and found it very promising. The second contribution of the paper involves an analysis of the incorporation of knowledge in CBR. This analysis provides a basis for classifying future interactions between CBR and other knowledge sources.