Improving data systems' performance for join operations has long been an issue of great importance. More recently, a lot of focus has been devoted to multi-way join performance and especially on reducing the negative impact of producing intermediate tuples, which in the end do not make it in the final result. We contribute a new multi-way join algorithm, coined SieveJoin, which extends the well-known Bloomjoin algorithm to multi-way joins and achieves state-of-the-art performance in terms of join query execution efficiency. SieveJoin's salient novel feature is that it allows the propagation of Bloom filters in the join path, enabling the system to `stop early' and eliminate useless intermediate join results. The key design objective of SieveJoin is to efficiently `learn' the join results, based on Bloom filters, with negligible memory overheads. We discuss the bottlenecks in delaying multi-way joins, and how Bloom filters are used to remove the generation of unnecessary intermediate join results. We provide a detailed experimental evaluation using various datasets, against a state-of-the-art column-store database and a multi-way worst-case optimal join algorithm, showcasing SieveJoin's gains in terms of response time.