The Toggle-based X-masking method requires a single toggle at a given cycle, there is a chance that non-Xvalues are also masked. Hence, the non-Xvalue over-masking problem may cause a fault coverage degradation. In this paper, a scan chain partitioning scheme is described to alleviate non-Xbit over-masking problem arising from Toggle-based X-Masking method. The scan chain partitioning method finds a scan chain combination that gives the least toggling conflicts. The experimental results show that the amount of over-masked bits is significantly reduced, and it is further reduced when the proposed method is incorporated with X-canceling method. However, as the number of scan chain partitions increases, the control data for decoder increases. To reduce a control data overhead, this paper exploits a Huffman coding based data compression. Assuming two partitions, the size of control bits is even smaller than the conventional X-toggling method that uses only one decoder. In addition, selection rules of X-bits delivered to X-Canceling MISR are also proposed. With the selection rules, a significant test time increase can be prevented.