Adapting keyword search to XML data has been attractive recently, generalized as XML keyword search (XKS). One of its key tasks is to return the meaningful fragments as the result. [1] is the latest work following this trend, and it focuses on returning the fragments rooted at SLCA (Smallest LCA – Lowest Common Ancestor) nodes. To guarantee that the fragments only contain interesting nodes, [1] proposes a contributor-based filtering mechanism in its MaxMatch algorithm. However, the filtering mechanism is not sufficient. It will commit the false positive problem (discarding interesting nodes) and the redundancy problem (keeping uninteresting nodes). In this paper, our interest is to propose a framework of retrieving meaningful fragments rooted at not only the SLCA nodes, but all LCA nodes. We begin by introducing the concept of Relaxed Tightest Fragment (RTF) as the basic result type. Then we propose a new filtering mechanism to overcome those two problems in MaxMatch. Its kernel...