The notion of tau-confluence provides a form of partial order reduction of Labelled Transition Systems (LTSs), by enabling to identify the tau-transitions whose execution does not alter the observable behaviour of the system. Several forms of tau-confluence adequate with branching bisimulation were studied in the literature, ranging from strong to weak forms according to the length of tau-transition sequences considered. Weak tau-confluence is more complex to compute than strong tau-confluence, but provides better LTS reductions. In this paper, we aim at devising an efficient detection of weak tau-confluent transitions during an on-the-fly exploration of LTSs. With this purpose, we define and prove new encodings of several weak tau-confluence variants using alternation-free Boolean equation systems (BESs), and we apply efficient local BES resolution algorithms to perform the detection. The resulting reduction module, developed within the CADP toolbox using the generic Open/Cæsar environment for LTS exploration, was tested in both a sequential and a distributed setting on numerous examples of large LTSs underpinning communication protocols and distributed systems. These experiments assessed the efficiency of the reduction and enabled us to identify the best variants of weak tau-confluence that are useful in practice.