Process for producing an injection water for an oil reservoir by pressurizing water having a total dissolved solids content of 20,000 to 45,000 ppm and a sulfate concentration of 1,000 to 4,000 ppm to 350 to 1250 psi absolute; and dividing the water into first and second feeds for reverse osmosis (RO) and nanofiltration (NF) units respectively. The units are operated in single-pass, single-stage mode or single-pass, two-stage mode, the NF permeate has a pressure at least 5 psi higher than the RO permeate, and the recoveries of the RO and NF permeates are 35 to 75% and 35 to 60% by volume respectively. RO permeate and NF permeate are mixed in a ratio of 2:1 to 40:1 to provide injection water having a TDS content of 500 to 5,000 ppm, and a sulfate concentration of less than 7.5 ppm.