Many current location-based applications (LBA) such as friend finder services use information about the positions of mobile users. So-called location services (LSs) have been proposed to manage these mobile user positions efficiently. However, managing user positions raises privacy issues, in particular, if the providers of LSs are only partially trusted. Therefore, the concept of private position sharing for partially trusted systems was proposed in the literature. The basic idea of position sharing is to split the precise user position into a set of position shares of well-defined limited precision and distribute these shares among LSs of different providers. The main contributions of this paper are two extended position sharing approaches that improve the basic position sharing approach in two ways: Firstly, we reduce the predictability of share generation that allows an attacker to gain further information from a sub-set of shares to further increase the position precision. Secondly, we present a position sharing algorithm for constrained movement scenarios whereas the existing approach was tailored to open space environments. However, open space approaches are vulnerable to map-based attacks. Therefore, we present a share generation algorithm that takes map knowledge into account.