Hedge funds have return peculiarities not commonly associated with traditional investment vehicles. Specifically, hedge funds seem more inclined to produce return distributions with significantly non-normal skewness and kurtosis. There is also growing acceptance of the notion that investor preferences are better represented by bilinear utility functions or S-shaped value functions than by neo-classical utility functions such as power utility. Many investors have therefore concluded that mean-variance optimization is not appropriate for forming portfolios that include hedge funds. We apply both mean-variance and full-scale optimization to form portfolios of hedge funds, given a wide range of assumptions about investor preferences. We find that higher moments of hedge funds do not meaningfully compromise the efficacy of mean-variance optimization if investors have power utility. We also find, however, that mean-variance optimization is not particularly effective for identifying optimal hedge fund allocations if preferences are bilinear or S-shaped. Finally, we show that investors with bilinear utility dislike kurtosis and that, contrary to conventional wisdom, investors with S-shaped preferences are attracted to kurtosis as well as negative skewness. Mean-variance optimization is insensitive to these preferences.