Bloom filter based algorithms have proven successful as very efficient technique to reduce communication costs of database joins in a distributed setting. However, the full potential of bloom filters has not yet been exploited. Especially in the case of multi-joins, where the data is distributed among several sites, additional optimization opportunities arise, which require new bloom filter operations and computations. In this paper, we present these extensions and point out how they improve the performance of such distributed joins. While the paper focuses on efficient join computation, the described extensions are applicable to a wide range of usages, where bloom filters are facilitated for compressed set representation.