We introduce a definition of constraint symmetry for soft CSPs, based on the definition of constraint symmetry for classical CSPs. We show that the constraint symmetry group of a soft CSP is a subgroup of that of an associated classical CSP instance. Where it is smaller, we can successfully exploit the additional symmetries using conditional symmetry breaking. We demonstrate, in a case-study of graph colouring, that eliminating the symmetry of the soft CSP combined with conditional symmetry breaking can lead to huge reductions in the search effort to find an optimal solution to the soft CSP. © Springer-Verlag Berlin Heidelberg 2007.