The classical Ellsberg experiment presents individuals with a choice problem in which the probability of winning a prize is unknown (uncertain). In this paper, we study how individuals make choices between gambles in which the uncertainty is in different dimensions: the winning probability, the amount of the prize, the payment date, and the combinations thereof. Although the decision-theoretic models accommodate a rich variety of behaviors, we present experimental evidence that points at systematic behavioral patterns: (i) no uncertainty is preferred to uncertainty on any single dimension and to uncertainty on multiple dimensions, and (ii) “correlated” uncertainty on multiple dimensions is preferred to uncertainty on any single dimension. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2015.2240 . This paper was accepted by Uri Gneezy, behavioral economics.