Much legal research focuses on understanding how judicial decisionmakers exercise their discretion. In this paper we examine the notion of legal or judicial discretion, and weaker and stronger forms of discretion. At all times our
goal is to build cognitive models of the exercise of discretion, with a view to building computer software to model and primarily support decision-making. We observe that discretionary decision-making can best be modeled using three independent axes: bounded and unbounded, defined and undefined, and binary and continuous. Examples of legal tasks are given from each of the eight ensuing
octants and we conclude by saying what this model shows about current legal trends. We should stress that our taxonomy has been based on our observations of how discretionary legal decisions are made. No claim is made that our model is either complete (providing advice in every domain) or exact, but it does help knowledge engineers construct legal decision support systems in discretionary domains.