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In order to compute lower bounds for shop scheduling problems, a lot of attention has been paid to adjustment techniques based on one-machine relaxations. We present such a new technique but, following the observation that machines are connected to each other through precedence constraints, we also study techniques that are based on the combination of precedence constraints and disjunctive constraints between operations that are processed on different machines. A computational study of the effectiveness of these new techniques is performed on job-shop and flow-shop instances.