This paper concerns the gage length dependence of fiber strength as established by measuring the fiber fracture stress vs. fragment length in the succession of fragments, which occur in tension testing of a single-fiber composite (s.f.c.). For fibers with a strength distribution described by a Weibull modulus m, a plot of in (fragment fracture stress) us. In(actual fragment length) leads to the deduction of an apparent Weibull modulus m(app) congruent to 0.63 m, whereas the apparently less rigorous procedure of plotting In (fragment fracture stress) vs. Ln (average fragment length) allows for accurate assessment of the true Weibull modulus. The m(app) textless m behavior arising from the use of actual fragment lengths occurs because fragments in the s.f.c. are not random sections of the fiber, but rather sections which have effectively been proof-tested at a stress corresponding to the strength of last fiber breaking stress occurring in the entire sample length. Hence, the individual fragments appear stronger than random fiber sections, leading to an apparently smaller Weibull modulus. Such complications do not arise if only the average fragment length, or equivalently the location-independent total number of breaks, is considered. Computer simulations of the fragmentation process verify analytic estimates of the ratio of m(app)/m, and demonstrate the accuracy of using the average fragment length to assess fiber Weibull modulus.