This thesis proposes an approach to improve test compression using sequential linear decompressors by using retained free variables. Sequential linear decompressors are inherently efficient and attractive for encoding test vectors with high percentages of don't cares (i.e., test cubes). The encoding of these test cubes is done by solving a system of linear equations. In streaming decompression, a fixed number of free variables are used to encode each test cube. The non-pivot free variables used in Gaussian Elimination are wasted when the decompressor is reset before encoding the next test cube which is conventionally done to keep computational complexity manageable. In this thesis, a technique for retaining the non-pivot free variables when encoding one test cube and using them in encoding the subsequent test cubes is explored. This approach retains most of the non-pivot free variables with a minimal increase in runtime for solving the equations. Also, no additional control information is needed. Experimental results are presented showing that the encoding efficiency and hence compression, can be significantly boosted. / text