We study a monopoly insurance model with endogenous information acquisi-
tion. Through a continuous effort choice, consumers can determine the precision of a privately observed signal that is informative about their accident risk. The equilibrium effort is, depending on parameter values, either zero (implying symmetric information) or positive (implying privately informed consumers). Regardless of the nature of the equilibrium, all offered contracts, also at the top, involve underinsurance, which discourages information gathering. We identify a missorting effect that explains why the insurer wants to discourage information acquisition. Moreover, lower information gathering costs can hurt both consumer and insurer.