This paper proposes an X-stacking technique for efficiently reducing the number of unknown values (X's) in the output response, thereby, in turn reducing the amount of control data required for output compaction without losing fault coverage. Output response streams containing X's are fed into circular registers, which stack X's on top of one another. The contents of the circular registers are then passed on to conventional output compaction circuitry where each stack of X's can then be treated as a single X thus substantially reducing the overall number of X's present in the output data thereby requiring less control data to perform output compaction. Some loss of observability may occur due to non-X values getting stacked with X values, but this can be compensated by adding some additional top-up test vectors. Results indicate that the overall test compression even with factoring in the additional test vectors is significantly improved with the proposed method. Different ways for implementing the circular registers, including configuring them from the scan cells themselves, are investigated for keeping the overhead for the proposed method very small.