The drainage capacity of cellulose pulps is an indicator of the surface conditions of the fibers, as well a measurable efficiency index of a refining process. The drainability depends on the refining process and the water quality. Temperature, pH and conductivity of water influence the drainability by affecting fiber and fines swelling; bleached chemical pulps are more sensitive to these variations. According to ISO 5267-2, the Canadian Standard Freeness (CSF) method provides a measure of the rate at which an aqueous suspension of pulp may be drained using deionized water, in a similar manner to the determination of the Schopper-Riegler grade (SR°). As different studies show, the variation in freeness of pulps is higher at conductivities near to zero than at higher conductivities. The objective of this study was to verify this behavior in Uruguayan pulps and to establish the conductivity values where the freeness stabilizes. This work examines the performance of the CSF and the SR° while the conductivity of a dilute suspension of pulp varies. The sample used is a Eucalyptus reference pulp, which is a Kraft bleached pulp. The conductivity was changed by adding different amounts of Magnesium Sulfate to deionized water in the suspensions. As expected, the results show a remarkable increase on the drainability values while the conductivity rises until a maximum value where it remains almost constant, despite the uprising in the conductivity. This study may be indicating the convenience of a modified CSF and SR method with high water conductivity where the variations are minimized.