Ellsberg and others suggested that ambiguity is a rich empirical domain with many phenomena to be investigated beyond the Ellsberg urns. We provide an empirical demonstration of this richness of ambiguity by varying both the outcomes, the (natural) events of uncertainty, and combinations of these. Although ambiguity aversion is prevailing, we also find systematic ambiguity seeking, confirming insensitivity (taking uncertainties as fifty-fifty). We find that ambiguity attitudes depend on the source of uncertainty (the kind of uncertain event) but not on the outcomes. Ambiguity attitudes are closer to rationality (ambiguity neutrality) for natural uncertainties than for the Ellsberg urns, as appearing from reductions of monotonicity violations and insensitivity, even under hypothetical choice. Our rich domain serves well to test which families of weighting functions are best suited for modeling ambiguity attitudes. Two-parameter families, capturing not only aversion but also insensitivity (“inverse-S”), are needed for ambiguity even more than for risk.