Test Method 58 was established by the International Wool Textile Organization in 2000 to analyze textile products made from specialty fibers, sheep's wool, and their blends. The method specifies the use of scanning electron microscopy to discriminate wool from all specialty fibers, such as cashmere, mohair, etc., mainly according to the cuticle scale height criterion. In this work, after the first step of the analysis, where 150 fibers are identified for their type, three cases are distinguished for which either a purity check, a two- component analysis by number, or a quantitative analysis of a two-component blend is conducted. The consequences of the thresholds separating the three cases are considered in detail for the first two cases. For various hypothetical samples of practical relevance, the minimum and maximum potential weight fractions of small admixtures are assessed. Extended analysis protocols are investigated, which enable the operator to sensibly adjust the course of a given analysis to its specific, technical, legal, and economic requirements.