Maps of completely proper rationality are introduced so as to parametrize departure from CARA decisionmaking in terms of level effects, and deepen the link between risk aversion, prudence and higher order concepts in connection with the objective approach to riskiness set forth by Aumann and Serrano (2008). On conceptual grounds, the focus on complete orders on preferences aligns with a line of progress of the microeconomics of risk. On technical grounds, the analytical tractability of our maps may prove effective in building explicit closed form solutions for relevant measures (for instance, the utility premium) in expected utility theory, as well as in conveying transparent insights concerning the relevance of complete properness.