Method for increasing the recovery of crude oil from a reservoir containing at least one porous and permeable subterranean formation wherein the formation includes sandstone rock and at least one mineral that has a negative zeta potential under the reservoir conditions and wherein crude oil and connate water are present within the pores of the formation. The method is carried out by (A) injecting into the formation a slug of an aqueous displacement fluid that displaces crude oil from the surface of the pores of the formation wherein the pore volume (PV) of the slug of the aqueous displacement fluid is at least 0.2 and less than 1 and the aqueous displacement fluid has a total dissolved solids (TDS) content in the range of 200 to 10,000 ppm and the fraction of the total multivalent cation content of the aqueous displacement fluid to the total multivalent cation content of the connate water is less than 1, and (B) subsequently injecting into the formation a drive water of higher multivalent cation content and/or higher total dissolved solids content than the aqueous displacement fluid.