Decentralized data fusion is a challenging task even for linear estimation problems. Nonlinear estimation renders data fusion even more difficult as dependencies among the nonlinear estimates require complicated parameterizations. It is nearly impossible to reconstruct or keep track of dependencies. Therefore, conservative approaches have become a popular solution to nonlinear data fusion. As a generalization of Covariance Intersection, exponential mixture densities have been widely applied for nonlinear fusion. However, this approach inherits the conservativeness of Covariance Intersection. For this reason, the less conservative fusion rule Inverse Covariance Intersection is studied in this paper and also generalized to nonlinear data fusion. This generalization employs a conservative approximation of the common information shared by the estimates to be fused. This bound of the common information is subtracted from the fusion result. In doing so, less conservative fusion results can be attained as an empirical analysis demonstrates.