An X-tolerant multiple-input signature register (MISR) compaction methodology that compacts output streams containing unknown (X) values, called X-canceling, is an alternative to masking X values (i.e., X-masking). A number of control bits that is linear in the number of X's to be canceled, are required to perform the X-canceling operation for existing Xcanceling approaches. This paper proposes a new X-canceling method significantly reducing the number of control bits for Xcanceling. We exploit the fact that 1) unknown values tend to be highly correlated in the scan cells (i.e., X's tend to be generated in certain portions of design) and 2) fault effects can typically be observed in a multiplicity of scan cells. Instead of custom generating the control bits to cancel out only the X's in one MISR signature, the proposed approach finds a general superset solution which can cancel out the X's for many MISR signatures without losing fault coverage. This allows the same control bits to be reused many times thereby significantly improving the amount of compression that can be obtained. Architectures for implementing superset X-canceling are described along with experimental results.