Unemployment insurance replacement rates world-wide are well below 100 percent, a fact often attributed to search moral hazard concerns. As Blanchard and Tirole (2008) have illustrated, however, neither search nor layoff moral hazard (firing cost) distortions need arise in first-best insurance plans. Their counterexample depends on the functional form of the state utility function--utility with a single argument, consumption plus monetized leisure. The monetized leisure model is unattractive if leisure is a choice variable, however, and a review of the optimal UI literature reveals a surprising variety of alternative utility function assumptions. A standard neoclassical utility function is used to characterize the utility function conditions required to generate moral-hazard-free (MHF) first-best contracts. Two conditions emerge: (i) the necessary condition that leisure and consumption be substitutes (the cross-derivative of consumption and leisure be negative) and (ii) the sufficient condition that leisure be an inferior good, Rosen (1985). Leisure appears to be a normal good, which rules out the possibility of first-best moral-hazard-free (FB MHF) utility structures, but the first-best UI replacement rate remains very much an open question. The rich empirical literature on the "retirement consumption paradox" suggests that the rate is below 100 percent, easing moral hazard concerns, if not eliminating them.