Multi-Context Systems (MCS ) are systems of distributed knowledge bases which interact via so called bridge rules. The MCSs we are interested in are nonmonotonic and therefore bridge rules can cause inconsistencies in the MCS while the knowledge bases for themselves are consistent. We will develop an algorithm which identifies those inconsistencies and proposes bridge rule modifications to the user which will make the system consistent. This algorithm will be effective with respect to requesting only as much information from the distributed knowledge bases as necessary. Therefore, for a user only interested in a part of the system, it is not necessary to know the whole system. We will show that this algorithm is sound and complete and present data demonstrating the performance of a reference implementation. To increase the performance of the algorithm we also propose further optimizations like edge and subset pruning and show the effectiveness of those modifications on the reference implementation.