It is well known that objectionable fibres emerge from the surface of the yarn due to the centrifugal force of the spinning device. Furthermore, the hair removal process is based on the same physical principles. However, the fibres that are >30 µm (PcF) are the fibres that appear in the hairiness of the yarn and are eliminated by dehairing. It has always been presumed that the PcF was linearly correlated with the diameter of the fibre (MFD) in llamas, but not so in alpaca fibres. Nevertheless, there is evidence that this relationship is curvilinear and behaves the same way in both species. The objectives of this study are to explore the relationship between MFD and PcF in both llamas and alpacas, to explore the existence of a breaking point (BP) in this curvilinear relationship, and to determine the frequency of fleeces that do not require dehairing because the PcF ≤ 3.2%. In addition, the existence of a positive bias of coarse fibre content on the hairy surface (CFs) of the yarn to coarse fibre content within the yarn fibres (CFy) was determined, which may explain the effect of the dehairing on the prickle factor of SAC fibres. The relationship of PcF on MFD behaves the same way in alpacas and llamas. It conforms to a power distribution and presents a BP of 23 µm, with PcF being constant before the BP and increasing significantly after it. Most animals (≤91% of alpacas and ≤87% of llamas) are above the threshold (≤3.2%), requiring dehairing to correct it. By means of a shaving technique on the surface of the fabric sample, it was established that the objectionable CFs content is 8.15% higher than the objectionable CFy content. In the evoked-coarse fibre in the dehaired samples, a CFs-CFy difference below 5.9% (p > 0.05) is not significantly detected by panellists. The surface MFD is more than 2.7 µm coarser than the yarn MFD.