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Determination of an efficient number of testing locations in multiple-location tests for cotton (Gossypium hirsutum L.) fiber quality can allow removal of unnecessary locations while maintaining the statistical power in detection of genotype (g) by environment (e) interactions. Fiber quality data from Regional High-Quality (RHQ) tests from 2011 to 2016 were used to determine an ef- ficient number of locations in the tests for fiber quality and relationships among locations for their representativeness and ability to discriminate among genotypes. Covariance parameters of g, location (l), and gl in the original RHQ tests were estimated in a random model. The simulating data with varying number of locations omitted from the original tests were created by performing 100 unique simulations. When locations were reduced to five, the standard deviations (std) of gl increased from 18 to 37% compared to the original tests. Further reduction of locations to four or less increased std of gl from 30 to 217% compared to the original tests. Therefore, five locations were determined to be an efficient number of locations in tests for fiber quality. The discriminating ability and representativeness of the eight locations for fiber properties were calculated as their distances to an "ideal environment", which was designed as a center in GGE biplot graphs for representativeness and discriminating ability. The relationships among locations were different across years. However, by averaging the distances across testing years, the locations of Stoneville, MS; Keiser, AR; Lubbock, TX; and College Station, TX were identified as the most representative testing sites for fiber properties. [ABSTRACT FROM AUTHOR]