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Excessive power dissipation during VLSI testing results in over-testing, yield loss and heat damage of the device. For low power devices with advanced power management features and more stringent power budgets, power-aware testing is even more mandatory. Effective and efficient test set postprocessing techniques based on X-identification and power-aware X-filling have been proposed for external and embedded deterministic test. This work proposes a novel X-filling algorithm for combinational and broadcast-scan-based test compression schemes which have great practical significance. The algorithm ensures compressibility of test cubes using a SAT-based check. Compared to methods based on topological justification, the solution space of the compressed test vector is not pruned early during the search. Thus, this method allows much more precise low-power X-filling of test vectors. Experiments on benchmark and industrial circuits show the applicability to capture-power reduction during scan testing.