While defect oriented testing in digital circuits is a hard process, detecting a modeled fault more than one time has been shown to result in high defect coverage. Previous workshows that such test sets, known as n-detect test sets, are of increased quality for a number of common defects in deep sub-micron technologies. n-detect test generation methods usually produce fully specified test patterns. This limits their usage in a number of important applications such as low power test and test compression. This work proposes a systematic methodology for identifying a large number of bits that can be unspecified in an n-detect test set, while preserving the n-detection property, in contrast to any other existing test set relaxation method. The experimental results demonstrate that the number of specified bits in, even compact, n-detect test sets can be significantly reduced without any impact on the n-detect property.