This paper makes observations regarding the extremization of entropy's production, and therefore available energy's destruction, in processes. The "case studies" given here were performed to gain insight, with a long-term goal of discovering a general extremization principle in thermodynamics (for example, a variational principle similar to Hamilton's principle, representing "the" equation of motion). The majority of these "case studies" are processes for which there are well known mathematical models. In several of them, entropy extremization has been recognized before. (C) 2004 Elsevier Ltd. All rights reserved.