Abstract Symmetries are common in many constraint problems. They can be broken statically or dynamically. The focus of this paper is the symmetry breaking during search (SBDS) method that adds conditional symmetry breaking constraints upon each backtracking during search. To trade completeness for efficiency, partial SBDS (ParSBDS) is proposed by posting only a subset of symmetries. We propose an adaptation method recursive SBDS (ReSBDS) of ParSBDS which extends ParSBDS to break more symmetry compositions. We observe that the symmetry breaking constraints added for each symmetry at a search node are nogoods and increasing. A global constraint (incNGs), which is logically equivalent to a set of increasing nogoods, is derived. To further trade pruning power for efficiency, we propose weak-nogood consistency (WNC) for nogoods and a lazy propagator for SBDS (and its variants) using watched literal technology. We further define generalized weak-incNGs consistency (GWIC) for a conjunction of increasing nogoods, and give a lazy propagator for incNGs. Recursive SBDS SBDS[Gent and Smith, 2000] leaves no symmetric solutions since all symmetries are given. For problems with exponential number of symmetries, direct use of SBDS is impractical [Gent and Smith, 2000]. To trade completeness for efficiency, partial SBDS (ParSBDS) is proposed by posting only a subset of symmetries [Petrie and Smith, 2003]. We prove that ParSBDS has the pitfall to leave more symmetric subtrees and solutions than the widely used static method LexLeader [Crawford et al., 1996] given the same subset of symmetries and the input-order variable and minimum (maximum) value heuristics. We propose Recursive SBDS (ReSBDS) [Lee and Zhu, 2014a] to circumvent the pitfall of ParSBDS. The main idea of ReSBDS is to addextra symmetry breaking constraints during search recur-sively to prune also symmetric nodes of some pruned subtrees. Thus, ReSBDS can break extra symmetry compositions. When given generators of interchangeable variables (values) according to a static search heuristic, ReSBDS is