Especially in the field of sensor networks and multi-robot systems, fully decentralized estimation techniques are of particular interest. As the required elimination of the complex dependencies between estimates generally yields inconsistent results, several approaches, e.g., covariance intersection, maintain consistency by providing conservative estimates. Unfortunately, these estimates are often too conservative and therefore, much less informative than a corresponding centralized approach. In this paper, we provide a concept that conservatively decorrelates the estimates while bounding the unknown correlations as closely as possible. For this purpose, known independent quantities, such as measurement noise, are explicitly identified and exploited. Based on tight covariance bounds, the new approach allows for an intuitive and systematic derivation of appropriate tailor-made filter equations and does not require heuristics. Its performance is demonstrated in a comparative study within a typical SLAM scenario.