Environmental and economic concerns are driving tissue paper manufacturers to improve understanding of the relationships between fibres, the networks they form, the forming process, and the final tissue paper properties. This work investigated how pulp fractionation, refining, or addition of microfibrillated cellulose (MFC) affect the compromise between absorbency and strength of 33 ± 2 g/m² model papers made of bleached eucalyptus kraft pulp. The results showed that the compromise of properties was better when fibres were refined than when MFC was added. The absorbency capacity of 2%wt MFC-paper was almost 20% lower than the capacity of the refined paper at the same dry strength. The calculated additional storage capacity due to water-induced deformations of the fibre network was 40% lower in the same range of bulk. By forming a high viscosity gel at inter-fibre contacts, MFC could limit the occurrence of major fibre and network deformation mechanisms when water was imbibing the paper.