Method and apparatus for cooling and/or liquefying a hydrocarbon stream

A refrigerant stream is provided at a refrigerant pressure, and passed through at least three heat exchange steps operating at different pressures. A hydrocarbon stream is passed through at least two of these heat exchange steps to provide a cooled stream. A fraction of the refrigerant stream is expanded and evaporated at each heat exchange step to a different pressure, to provide a first evaporated refrigerant stream at a first evaporation pressure, and at least two other evaporated refrigerant streams at evaporation pressures lower than the first. The first evaporated refrigerant stream is compressed through a highest-pressure compressor to provide at least a fraction of the refrigerant stream at the refrigerant pressure, and the other evaporated refrigerant streams are compressed through at least two parallel lower pressure compressors to provide two or more part-compressed refrigerant streams, all of which part-compressed refrigerant streams are passed through the highest pressure compressor.