In this study, a new technique for producing almost fully aligned paper sheets was developed, and the resulting sheets were used to test the validity of the theory most commonly used to relate zero-span tensile strength to individual ﬁbre strength. The standard theory predicts that a zero-span test of a sheet with randomly oriented ﬁbres should yield a breaking load equal to 3/8 of the load that would be observed if all the ﬁbres were aligned in the direction of loading. It is widely used, in spite of the fact that the underlying assumption of afﬁne deformation is questionable under true zero-span conditions. The results obtained here suggest that the ﬁbre strength may be overestimated because inclined ﬁbres in a zero-span grip actually contribute more than the theory predicts. However, the results also suggest that this effect may be confounded because other factors lead to a variable contribution of individual ﬁbres to the zero-span strength of the sheet.