Abstract: A process and apparatus for the preparation of improved cellulose pulps is provided, in which defibered pulp is screened for removal of shives, and fibers with low bonding ability are removed in hydrocyclones, and rejects from the hydrocyclones are treated in refiner. In the process a specific combination of characteristics for the hydrocyclones and the volumetric flow is used in order to prepare pulps which give products of improved qualities, such as higher tensile strength, tear strength, light-scattering, surface smoothness, and especially low shive content.