Since Rothschild and Stiglitz (1976), RS, asymmetric information is considered to be a potential setback in insurance markets, particularly so in health insurance, due to adverse selection. However, many empirical works find no evidence of adverse selection. The recent literature establishes that failure to find evidence of adverse selection may be due to the multidimensional heterogeneity of individuals’ characteristics. In this recent literature, one of the proposed (additional) dimensions of heterogeneity is directly relevant for the insuree only: risk aversion, cognitive ability, or misperceptions on risk. We instead analyze a different source of multidimensionality, namely, the presence of more than one source of risk. In our particular application, two sources of risk exist: (1) needing inpatient care and (2) needing outpatient care. Notice that these dimensions are not only directly relevant to the insuree but also to the insurer. This extension is important for at least four reasons: a) individuals may have different risk profiles along these dimensions, implying that risks may not be ranked; b) insurance contracts may have different degrees of coverage along these two dimensions; c) there may be asymmetric information in one risk dimension and not in the other; (d) and most importantly, adverse selection may be underestimated if one takes aggregate measures of risk an coverage in order to reduce the analysis to one of single dimensional screening. We start by extending the competitive separating equilibrium of RS to allow for two sources of risk and two-dimensional coverage contracts and use its theoretical predictions to construct an alternative test of asymmetric information, which we apply to the universe of the privately insured in the Chilean health insurance market for the year 2007.