Continuous spatial queries posted within an environment of moving objects produce as their results a time-varying set of objects. In the most ambitious case both queries and data objects are dynamic, making it very challenging to find an efficient query evaluation strategy. The significant overhead related to frequent location updates from moving objects often results in poor performance. The most advanced existing techniques use the concept of simple geometric safe regions to delay or avoid location updates. We introduce a Partition-based Lazy Update (PLU) algorithm that elevates this idea further by adopting Location Information Tables (LIT) which (a) allow each moving object to estimate possible query movements and issue a location update only when it may affect any query results and (b) enable smart server probing that results in fewer messages. Among the significant advantages, our technique performs well even in very highly dynamic environments (with up to 100% mobility) where m...