Constraint Logic Programming (CLP) and Abductive Logic Programming (ALP) share the important concept of conditional answer. We exploit their deep similarities to implement an efficient abductive solver where abducibles are treated as constraints. We propose two possible implementations, in which integrity constraints are exploited either (i) as the definition of a CLP solver on an abductive domain, or (ii) as constraints à la CLP. Both the solvers are implemented on top of CLP(Bool), that typically have impressively efficient propagation engines.