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Many novel location-based services (LBS) such as a friend finder service require knowledge about the positions of mobile users. Usually, location services are used to manage these positions, and for providing basic functionality like spatial range queries or spatial events to the LBS. Managing and using the positions of mobile users raises privacy issues, in particular, if the providers of LBS and location services are only partially trusted. Many different approaches for preserving a user's privacy have been proposed in the literature, e.g. location obfuscation and the k-anonymity concept. However, most of them are not suitable if both LBS and location service providers are non-trusted. In contrast to these approaches, we present a novel approach for the secure management of private position information in partially trusted system environments. The main contribution in this paper is a position sharing concept which allows for the distribution of position information (shares) of strictly limited accuracy onto several location servers of different providers. With this approach, a compromised server will only reveal information of limited accuracy. Moreover, we will show how position shares of coarse granularity from multiple location servers can be fused into information of higher precision to satisfy the accuracy requirements of different LBS.